instruction_seed stringlengths 36 975 | response_seed stringlengths 80 10.9k | reasoning stringlengths 381 100k | deepseek_solution stringlengths 29 15.4k | __original_row_idx int64 0 34.6k | source stringclasses 1
value | final_reasoning_trace stringlengths 744 102k | conversations listlengths 2 2 |
|---|---|---|---|---|---|---|---|
Mr. Adams measures his rectangular orchard and finds it is 25 steps by X steps. Each of Mr. Adams's steps is 2 feet long. He anticipates 0.3 pounds of apples per square foot from his orchard. What is Mr. Adams's expected yield of apples? If we know the answer to the above question is 900, what is the value of unknown v... | To solve this problem, we first need to determine the area of Mr. Adams's rectangular orchard, which will allow us to calculate the expected yield of apples based on the anticipated yield per square foot.
1. **Convert the dimensions from steps to feet:**
- Width of the orchard in feet = 25 steps * 2 feet/step = ... | Okay, let's see. Mr. Adams has a rectangular orchard, and he measures it as 25 steps by X steps. Each step is 2 feet long. So, first, I need to figure out the area of the orchard in square feet because the yield is given in pounds per square foot. The expected yield is 0.3 pounds per square foot, and the answer is supp... | Mr. Adams's orchard is measured as 25 steps by \( X \) steps. Each step is 2 feet long. To find the area of the orchard in square feet, we convert the steps to feet:
- Length: \( 25 \) steps \( \times 2 \) feet/step = \( 50 \) feet
- Width: \( X \) steps \( \times 2 \) feet/step = \( 2X \) feet
The area of the orchar... | 0 | MetaMath-AIME | <think>
Okay, let's see. Mr. Adams has a rectangular orchard, and he measures it as 25 steps by X steps. Each step is 2 feet long. So, first, I need to figure out the area of the orchard in square feet because the yield is given in pounds per square foot. The expected yield is 0.3 pounds per square foot, and the answer... | [
{
"from": "human",
"value": "Mr. Adams measures his rectangular orchard and finds it is 25 steps by X steps. Each of Mr. Adams's steps is 2 feet long. He anticipates 0.3 pounds of apples per square foot from his orchard. What is Mr. Adams's expected yield of apples? If we know the answer to the above questi... |
Let u and v be the smallest positive integers such that the product of 600 with u is a perfect square and the product of 600 with v is a perfect cube. What is the sum of u and v? | To solve for the smallest positive integers \( u \) and \( v \) such that \( 600u \) is a perfect square and \( 600v \) is a perfect cube, we first need to find the prime factorization of 600.
The prime factorization of 600 is:
\[ 600 = 2^3 \times 3^1 \times 5^2 \]
### Step 1: Finding \( u \) for a perfect square... | Okay, let's see. I need to find the smallest positive integers u and v such that 600 multiplied by u is a perfect square and 600 multiplied by v is a perfect cube. Then, I have to add u and v together. Hmm, okay. I remember something about prime factorization for these kinds of problems. Let me try to recall.
First, m... | To find the smallest positive integers \( u \) and \( v \) such that \( 600u \) is a perfect square and \( 600v \) is a perfect cube, we start by factorizing 600 into its prime components:
\[
600 = 2^3 \times 3^1 \times 5^2
\]
For \( 600u \) to be a perfect square, all the exponents in the prime factorization must be... | 2 | MetaMath-AIME | <think>
Okay, let's see. I need to find the smallest positive integers u and v such that 600 multiplied by u is a perfect square and 600 multiplied by v is a perfect cube. Then, I have to add u and v together. Hmm, okay. I remember something about prime factorization for these kinds of problems. Let me try to recall.
... | [
{
"from": "human",
"value": "Let u and v be the smallest positive integers such that the product of 600 with u is a perfect square and the product of 600 with v is a perfect cube. What is the sum of u and v?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. I need to find the smallest pos... |
Liam has 4 peaches and 8 cherries. He extracts 8 ounces of cherry juice from 4 cherries and X ounces of peach juice from 2 peaches. If he blends an equal number of peaches and cherries, what percent of the blend is cherry juice? If we know the answer to the above question is 33.33, what is the value of unknown variable... | To solve this problem, we need to determine the value of X, which represents the ounces of peach juice extracted from 2 peaches. We will also find out the percentage of cherry juice in the blend of peaches and cherries.
Let's break down the information given:
- Liam has 4 peaches and 8 cherries.
- The juice extracted ... | Alright, let's tackle this problem step by step. So, Liam has 4 peaches and 8 cherries. He makes cherry juice from 4 cherries, getting 8 ounces, and peach juice from 2 peaches, getting X ounces. Then he blends an equal number of peaches and cherries. We need to find X such that the blend is 33.33% cherry juice. Hmm, ok... | Liam has 4 peaches and 8 cherries. He extracts 8 ounces of cherry juice from 4 cherries and \( X \) ounces of peach juice from 2 peaches. We need to find \( X \) such that the blend of an equal number of peaches and cherries results in 33.33% cherry juice.
1. **Juice Extraction Details:**
- Cherry juice: 8 ounces f... | 1 | MetaMath-AIME | <think>
Alright, let's tackle this problem step by step. So, Liam has 4 peaches and 8 cherries. He makes cherry juice from 4 cherries, getting 8 ounces, and peach juice from 2 peaches, getting X ounces. Then he blends an equal number of peaches and cherries. We need to find X such that the blend is 33.33% cherry juice.... | [
{
"from": "human",
"value": "Liam has 4 peaches and 8 cherries. He extracts 8 ounces of cherry juice from 4 cherries and X ounces of peach juice from 2 peaches. If he blends an equal number of peaches and cherries, what percent of the blend is cherry juice? If we know the answer to the above question is 33.... |
At a reunion of 38 people, 18 know each other while X are strangers. There are 550 handshakes that occur at the reunion. What is the value of the unknown variable X? | To solve this problem, we need to determine the value of X, which represents the number of people who are strangers at the reunion.
Let's break down the information given:
- Total number of people at the reunion = 38
- Number of people who know each other = 18
- Therefore, number of strangers (X) = 38 - 18 = 20.
Now,... | Okay, let me try to figure out this problem. So, there's a reunion with 38 people. Out of these, 18 know each other, and X are strangers. They mention that there are 550 handshakes happening. I need to find the value of X. Hmm, let me start breaking this down step by step.
First, I remember that in problems involving ... | To solve the problem, we need to determine the number of strangers \( X \) at a reunion of 38 people where 550 handshakes occur. Here are the key steps:
1. **Total possible handshakes**: The total number of possible handshakes among 38 people is calculated using the combination formula \( \binom{38}{2} \):
\[
\b... | 3 | MetaMath-AIME | <think>
Okay, let me try to figure out this problem. So, there's a reunion with 38 people. Out of these, 18 know each other, and X are strangers. They mention that there are 550 handshakes happening. I need to find the value of X. Hmm, let me start breaking this down step by step.
First, I remember that in problems in... | [
{
"from": "human",
"value": "At a reunion of 38 people, 18 know each other while X are strangers. There are 550 handshakes that occur at the reunion. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let me try to figure out this problem. So, there's a re... |
A bag contains X green marbles and 6 red marbles. The probability that both marbles drawn are red is 15/28. What is the value of the unknown variable X? | To solve this problem, we need to calculate the probability of drawing two red marbles from a bag that contains X green marbles and 6 red marbles.
First, we need to find the total number of marbles in the bag. Since there are X green marbles and 6 red marbles, the total number of marbles is:
Total = X + 6
The proba... | Okay, so I need to figure out how many green marbles are in the bag. The problem says there are X green marbles and 6 red marbles. When you draw two marbles without replacement, the probability that both are red is 15/28. Hmm, okay. Let me remember how probability works with combinations.
First, the total number of ma... | The problem involves determining the number of green marbles, \( X \), in a bag containing \( X \) green marbles and 6 red marbles. The probability of drawing two red marbles is given as \( \frac{15}{28} \).
First, we calculate the probability of drawing two red marbles. The total number of marbles is \( X + 6 \). The... | 6 | MetaMath-AIME | <think>
Okay, so I need to figure out how many green marbles are in the bag. The problem says there are X green marbles and 6 red marbles. When you draw two marbles without replacement, the probability that both are red is 15/28. Hmm, okay. Let me remember how probability works with combinations.
First, the total numb... | [
{
"from": "human",
"value": "A bag contains X green marbles and 6 red marbles. The probability that both marbles drawn are red is 15/28. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out how many green marbles are in the bag. The p... |
In a plane, if five lines are drawn such that no two lines are parallel and no three lines intersect at the same point, how many regions are created? | Let's solve this problem step by step by focusing on the number of lines added and how they divide the plane into regions.
1. **Base case**: A single line divides the plane into 2 regions.
- If there are 1 line: 2 regions.
2. **Adding a second line**: A second line that intersects the first creates 2 additiona... | Okay, so I need to figure out how many regions five lines create in a plane, given that no two lines are parallel and no three lines meet at the same point. Hmm, let me start by visualizing this. Maybe drawing a few lines and counting the regions each time. But since I can't actually draw here, I'll try to recall if th... | To determine the number of regions created by five lines in a plane, where no two lines are parallel and no three lines intersect at the same point, we use the formula for the maximum number of regions defined by \( n \) lines:
\[
R(n) = \frac{n(n + 1)}{2} + 1
\]
We start by verifying the formula with smaller values... | 5 | MetaMath-AIME | <think>
Okay, so I need to figure out how many regions five lines create in a plane, given that no two lines are parallel and no three lines meet at the same point. Hmm, let me start by visualizing this. Maybe drawing a few lines and counting the regions each time. But since I can't actually draw here, I'll try to reca... | [
{
"from": "human",
"value": "In a plane, if five lines are drawn such that no two lines are parallel and no three lines intersect at the same point, how many regions are created?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out how many regions five lines create in a plane, ... |
A circle of diameter 4 is removed from a 5 × X rectangle. The whole number closest to the area of the shaded region is 37. What is the value of the unknown variable X? | To solve this problem, we need to determine the area of the shaded region in the rectangle after the circle is removed, and find the value of X such that the area of the shaded region is closest to 37.
1. **Calculate the area of the circle:**
- The diameter of the circle is 4, so the radius (r) is 4 / 2 = 2.
... | Okay, let's see. I need to find the value of X in a 5 by X rectangle from which a circle of diameter 4 has been removed. The area of the shaded region (which is the rectangle minus the circle) is closest to 37, and we need to find X. Hmm, let me break this down step by step.
First, the area of the rectangle is length ... | To find the value of \( X \) in a \( 5 \times X \) rectangle from which a circle of diameter 4 has been removed, we start by calculating the area of the rectangle and the circle. The area of the rectangle is \( 5X \). The circle has a radius of 2 (since the diameter is 4), so its area is \( 4\pi \).
The area of the sh... | 4 | MetaMath-AIME | <think>
Okay, let's see. I need to find the value of X in a 5 by X rectangle from which a circle of diameter 4 has been removed. The area of the shaded region (which is the rectangle minus the circle) is closest to 37, and we need to find X. Hmm, let me break this down step by step.
First, the area of the rectangle is... | [
{
"from": "human",
"value": "A circle of diameter 4 is removed from a 5 × X rectangle. The whole number closest to the area of the shaded region is 37. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. I need to find the value of X in a 5 by X ... |
A turtle starts from a corner of a square with side length X meters. It moves 6.4 meters along a diagonal towards the opposite corner, then makes a 90^{ } right turn and moves 2.5 meters. What is the average distance from the turtle to each side of the square? If we know the answer to the above question is 4.5, what is... | To solve this problem, we need to determine the location of the turtle after it has moved along the diagonal of the square and then turned and moved a certain distance. Additionally, we need to use the information about the average distance from the turtle to each side of the square in order to find the value of X.
1.... | Okay, let me try to figure this problem out. So, there's a square with side length X meters. A turtle starts from one corner and moves 6.4 meters along the diagonal towards the opposite corner. Then it makes a 90-degree right turn and moves 2.5 meters. We need to find the average distance from the turtle's final positi... | The turtle starts from a corner of a square with side length \( X \) meters and moves 6.4 meters along the diagonal towards the opposite corner. The coordinates after this movement are \( \left( \frac{6.4}{\sqrt{2}}, \frac{6.4}{\sqrt{2}} \right) \). The turtle then makes a 90-degree right turn and moves 2.5 meters in t... | 7 | MetaMath-AIME | <think>
Okay, let me try to figure this problem out. So, there's a square with side length X meters. A turtle starts from one corner and moves 6.4 meters along the diagonal towards the opposite corner. Then it makes a 90-degree right turn and moves 2.5 meters. We need to find the average distance from the turtle's fina... | [
{
"from": "human",
"value": "A turtle starts from a corner of a square with side length X meters. It moves 6.4 meters along a diagonal towards the opposite corner, then makes a 90^{\u0000} right turn and moves 2.5 meters. What is the average distance from the turtle to each side of the square? If we know th... |
In a baseball game, the Red Sox and the Yankees scored a total of 62 points, with the Red Sox winning by X points. The Yankees scored 18 points. What is the value of the unknown variable X? | To solve this problem, we need to determine the value of X, which represents the number of points by which the Red Sox won the game.
Let's break down the information given:
- Total points scored by both teams: 62 points
- Points scored by the Yankees: 18 points
- Points scored by the Red Sox = Points scored by the Y... | Okay, so I need to figure out by how many points the Red Sox won against the Yankees. The total score for both teams is 62 points, and the Yankees scored 18 points. Let me think step by step.
First, if the total is 62 and the Yankees scored 18, then the Red Sox must have scored the rest. So, to find the Red Sox's scor... | The total score of the game is 62 points. The Yankees scored 18 points, so the Red Sox scored:
\[
62 - 18 = 44 \text{ points}
\]
The value of \( X \) (the margin of victory) is the difference between the Red Sox's score and the Yankees's score:
\[
X = 44 - 18 = 26
\]
**Answer:** \(\boxed{26}\) | 682 | MetaMath-AIME | <think>
Okay, so I need to figure out by how many points the Red Sox won against the Yankees. The total score for both teams is 62 points, and the Yankees scored 18 points. Let me think step by step.
First, if the total is 62 and the Yankees scored 18, then the Red Sox must have scored the rest. So, to find the Red So... | [
{
"from": "human",
"value": "In a baseball game, the Red Sox and the Yankees scored a total of 62 points, with the Red Sox winning by X points. The Yankees scored 18 points. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out by how ... |
If Olivia's car has a fuel efficiency of 35 miles per gallon and gas is priced at $4.50 per gallon, how many miles can she travel with a budget of $45? | To find out how many miles Olivia can travel with a budget of $45, we can follow these steps:
1. **Determine how many gallons of gas she can buy with $45**:
- The cost of gas is $4.50 per gallon.
- To find the number of gallons she can purchase, we divide her budget by the price per gallon:
\[ \text{Gallons... | Okay, let's see. Olivia has $45 to spend on gas, and each gallon costs $4.50. Her car can go 35 miles on one gallon. So, I need to figure out how many gallons she can buy with $45 and then multiply that by the fuel efficiency to get the total miles.
First, let's calculate the number of gallons she can purchase. If one... | To determine how many miles Olivia can travel with a budget of $45, we first calculate how many gallons of gas she can purchase. Given the price of gas is $4.50 per gallon, we divide her budget by the price per gallon:
\[
\frac{45}{4.50} = 10 \text{ gallons}
\]
Next, we use her car's fuel efficiency of 35 miles per g... | 1,234 | MetaMath-AIME | <think>
Okay, let's see. Olivia has $45 to spend on gas, and each gallon costs $4.50. Her car can go 35 miles on one gallon. So, I need to figure out how many gallons she can buy with $45 and then multiply that by the fuel efficiency to get the total miles.
First, let's calculate the number of gallons she can purchase... | [
{
"from": "human",
"value": "If Olivia's car has a fuel efficiency of 35 miles per gallon and gas is priced at $4.50 per gallon, how many miles can she travel with a budget of $45?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. Olivia has $45 to spend on gas, and each gallon costs $4.5... |
Ryan owns 2 wooden crates, each with a weight of 15 kg, while Ava has 5 wooden crates, each weighing 10 kg. What is the combined weight of all 7 crates? | First, we will calculate the total weight of Ryan's crates.
Ryan has 2 crates, each weighing 15 kg.
So, the total weight of Ryan's crates is:
\(2 \text{ crates} \times 15 \text{ kg/crate} = 30 \text{ kg}.\)
Next, we will calculate the total weight of Ava's crates.
Ava has 5 crates, each weighing 10 kg.
So, the to... | Okay, so Ryan has two wooden crates, each weighing 15 kg. Let me write that down. Ryan's crates: 2 crates × 15 kg each. Hmm, to find the total weight for Ryan's crates, I need to multiply the number of crates by the weight per crate. So that's 2 times 15. Let me calculate that. 15 plus 15 is 30, so 2 × 15 = 30 kg. Got ... | Ryan's 2 crates weigh \(2 \times 15 = 30\) kg.
Ava's 5 crates weigh \(5 \times 10 = 50\) kg.
Combined, all 7 crates total \(30 + 50 = 80\) kg.
**Answer:** The combined weight is \(\boxed{80}\) kilograms. | 238 | MetaMath-AIME | <think>
Okay, so Ryan has two wooden crates, each weighing 15 kg. Let me write that down. Ryan's crates: 2 crates × 15 kg each. Hmm, to find the total weight for Ryan's crates, I need to multiply the number of crates by the weight per crate. So that's 2 times 15. Let me calculate that. 15 plus 15 is 30, so 2 × 15 = 30 ... | [
{
"from": "human",
"value": "Ryan owns 2 wooden crates, each with a weight of 15 kg, while Ava has 5 wooden crates, each weighing 10 kg. What is the combined weight of all 7 crates?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so Ryan has two wooden crates, each weighing 15 kg. Let me write tha... |
What is the difference in the sales tax amount between a 9.5% tax and an 8.5% tax on an item that is priced at $100 before tax? | To calculate the difference in sales tax amounts between a 9.5% tax and an 8.5% tax on a $100 item, we can proceed with the following steps:
1. **Calculate the 9.5% sales tax**:
- Sales Tax = Price × Tax Rate
- Sales Tax for 9.5% = $100 × 0.095 = $9.50
2. **Calculate the 8.5% sales tax**:
- Sales Tax for 8.5... | Okay, let's see. The problem is asking for the difference in sales tax amount between a 9.5% tax and an 8.5% tax on a $100 item. Hmm, right. So, first, I need to calculate both taxes separately and then find the difference between them.
Alright, starting with the 9.5% tax. To find out how much tax that is on $100, I ... | The difference in the sales tax amount between a 9.5% tax and an 8.5% tax on a $100 item is calculated as follows:
1. **Calculate 9.5% tax**:
\( 100 \times 0.095 = \$9.50 \)
2. **Calculate 8.5% tax**:
\( 100 \times 0.085 = \$8.50 \)
3. **Find the difference**:
\( \$9.50 - \$8.50 = \$1.00 \)
**Answer:... | 857 | MetaMath-AIME | <think>
Okay, let's see. The problem is asking for the difference in sales tax amount between a 9.5% tax and an 8.5% tax on a $100 item. Hmm, right. So, first, I need to calculate both taxes separately and then find the difference between them.
Alright, starting with the 9.5% tax. To find out how much tax that is on ... | [
{
"from": "human",
"value": "What is the difference in the sales tax amount between a 9.5% tax and an 8.5% tax on an item that is priced at $100 before tax?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. The problem is asking for the difference in sales tax amount between a 9.5% tax an... |
What is the percentage increase in the price of a smartphone that rose from $600 in 2015 to $800 in 2022? | To calculate the percentage increase in the price of the smartphone from 2015 to 2022, we can use the formula:
\[ \text{Percentage Increase} = \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \times 100 \% \]
1. **Identify the old and new prices**:
- Old Price (2015) = $600
- New Price (2022)... | Okay, so I need to find the percentage increase in the price of a smartphone from 2015 to 2022. The price went up from $600 to $800. Let me think about how to calculate percentage increase.
First, percentage increase is calculated by taking the difference between the new price and the original price, then dividing th... | The percentage increase in the price of the smartphone is calculated as follows:
1. **Determine the difference in price**:
$800 (2022 price) - $600 (2015 price) = **$200**
2. **Divide the difference by the original price**:
$200 ÷ $600 = **⅓** ≈ 0.3333
3. **Convert to a percentage**:
0.3333 × 100 = **... | 522 | MetaMath-AIME | <think>
Okay, so I need to find the percentage increase in the price of a smartphone from 2015 to 2022. The price went up from $600 to $800. Let me think about how to calculate percentage increase.
First, percentage increase is calculated by taking the difference between the new price and the original price, then div... | [
{
"from": "human",
"value": "What is the percentage increase in the price of a smartphone that rose from $600 in 2015 to $800 in 2022?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the percentage increase in the price of a smartphone from 2015 to 2022. The price went up from $6... |
Elena practices yoga and initially completed 5 cycles of asanas in 15 minutes. Now, she can finish 6 cycles in 12 minutes. How many minutes has her time per cycle improved? | 1. **Calculate Elena's initial time per cycle:**
- Initial cycles completed: 5 cycles
- Initial time taken: 15 minutes
- Initial time per cycle = Total time / Number of cycles = 15 minutes / 5 cycles = 3 minutes per cycle.
2. **Calculate her current time per cycle:**
- Current cycles completed: 6 c... | Okay, so Elena does yoga, right? And the problem says she initially did 5 cycles of asanas in 15 minutes. Now, she can finish 6 cycles in 12 minutes. The question is asking how many minutes her time per cycle has improved. Hmm, improved meaning she's faster now, so her time per cycle has decreased. We need to find the ... | Initially, Elena completed 5 cycles of asanas in 15 minutes. To find her original time per cycle, we divide the total time by the number of cycles:
\[
\frac{15 \text{ minutes}}{5 \text{ cycles}} = 3 \text{ minutes per cycle}
\]
Now, she can finish 6 cycles in 12 minutes. To find her new time per cycle, we divide the t... | 488 | MetaMath-AIME | <think>
Okay, so Elena does yoga, right? And the problem says she initially did 5 cycles of asanas in 15 minutes. Now, she can finish 6 cycles in 12 minutes. The question is asking how many minutes her time per cycle has improved. Hmm, improved meaning she's faster now, so her time per cycle has decreased. We need to f... | [
{
"from": "human",
"value": "Elena practices yoga and initially completed 5 cycles of asanas in 15 minutes. Now, she can finish 6 cycles in 12 minutes. How many minutes has her time per cycle improved?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so Elena does yoga, right? And the problem says ... |
At a bookstore: "Buy 4 novels at the standard price and get the fifth one for X dollars." Rachel spent 107 dollars on five novels. The standard price of one novel was 25. What is the value of the unknown variable X? | To solve this problem, we need to break down the total cost of the novels purchased by Rachel and determine the value of the unknown variable X, which represents the price she paid for the fifth novel.
1. **Calculate the cost of the first four novels:**
The standard price of one novel is $25. Therefore, the cost ... | Okay, let's see. So Rachel bought five novels at the bookstore. The deal is "Buy 4 novels at the standard price and get the fifth one for X dollars." She spent a total of 107 dollars. The standard price of one novel is 25 dollars. We need to find out what X is.
Alright, let's break this down. First, the standard price... | Rachel bought five novels under a promotion where buying 4 novels at the standard price allows her to get the fifth one for \( X \) dollars. The standard price of one novel is 25 dollars.
First, calculate the cost of 4 novels at the standard price:
\[
4 \times 25 = 100 \text{ dollars}
\]
The total amount Rachel spen... | 165 | MetaMath-AIME | <think>
Okay, let's see. So Rachel bought five novels at the bookstore. The deal is "Buy 4 novels at the standard price and get the fifth one for X dollars." She spent a total of 107 dollars. The standard price of one novel is 25 dollars. We need to find out what X is.
Alright, let's break this down. First, the standa... | [
{
"from": "human",
"value": "At a bookstore: \"Buy 4 novels at the standard price and get the fifth one for X dollars.\" Rachel spent 107 dollars on five novels. The standard price of one novel was 25. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let... |
An internet service costs $50 monthly, $1 for every GB of data used beyond X GB. In April, Alex used 120 GB of data. He owes 70 this month. What is the value of the unknown variable X? | To solve this problem, we need to establish an equation based on the costs incurred by Alex for his internet usage this month.
1. **Monthly fixed cost**: $50
2. **Data used**: 120 GB
3. **Total owed**: $70
4. **Additional cost for data beyond X GB**: $1 for each GB over X GB.
Given that Alex's total charge is $7... | Okay, let's see. Alex's internet service costs $50 a month, and then if he goes over a certain amount of data, X GB, he has to pay $1 for every GB beyond that. In April, he used 120 GB and his total bill was $70. We need to find X, the data allowance before extra charges kick in.
First, the base cost is $50, regardles... | Alex's internet service has a base cost of $50 per month and charges $1 for every GB of data used beyond X GB. In April, Alex used 120 GB of data and owed $70.
To find X, we start by noting the total bill is the sum of the base cost and the overage charges. The overage charges are calculated as $1 per GB for data use... | 297 | MetaMath-AIME | <think>
Okay, let's see. Alex's internet service costs $50 a month, and then if he goes over a certain amount of data, X GB, he has to pay $1 for every GB beyond that. In April, he used 120 GB and his total bill was $70. We need to find X, the data allowance before extra charges kick in.
First, the base cost is $50, r... | [
{
"from": "human",
"value": "An internet service costs $50 monthly, $1 for every GB of data used beyond X GB. In April, Alex used 120 GB of data. He owes 70 this month. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. Alex's internet service c... |
Ethan needs to take one orange tablet and one yellow tablet daily for X days. The orange tablet costs $2 more than the yellow tablet, and the total expenditure is $112. What is the price of one orange tablet? If we know the answer to the above question is 8, what is the value of unknown variable X? | To solve this problem, we need to determine the value of X, which represents the number of days Ethan needs to take the tablets.
Let's break down the information given:
- Cost of one orange tablet: O
- Cost of one yellow tablet: Y
- O = Y + $2 (since the orange tablet costs $2 more than the yellow tablet)
- Total exp... | Okay, let me try to figure this out. So Ethan is taking two different tablets each day: one orange and one yellow. He does this for X days. The total cost over those X days is $112. The orange tablet is $2 more expensive than the yellow one. And we need to find out how many days he took them, X, given that the price of... | Given that Ethan needs to take one orange tablet and one yellow tablet daily for \( X \) days, and the total expenditure is $112, we need to find the value of \( X \) given that the price of one orange tablet is $8.
1. The price of the orange tablet is $8.
2. The price of the yellow tablet, which is $2 less than the o... | 718 | MetaMath-AIME | <think>
Okay, let me try to figure this out. So Ethan is taking two different tablets each day: one orange and one yellow. He does this for X days. The total cost over those X days is $112. The orange tablet is $2 more expensive than the yellow one. And we need to find out how many days he took them, X, given that the ... | [
{
"from": "human",
"value": "Ethan needs to take one orange tablet and one yellow tablet daily for X days. The orange tablet costs $2 more than the yellow tablet, and the total expenditure is $112. What is the price of one orange tablet? If we know the answer to the above question is 8, what is the value of... |
Laura is 6 years younger than Ethan. Ethan is 4 years older than Mia. Mia is X years old. Laura is 8 years old. What is the value of the unknown variable X? | To solve this problem, we first need to determine the ages of each person based on the information given. Let's break it down step by step:
1. We know that Laura is 8 years old.
2. We are told that Laura is 6 years younger than Ethan. Therefore, we can find Ethan's age:
- Ethan's age = Laura's age + 6 = 8 + 6 = 14 ... | Okay, let's see here. The problem is about figuring out Mia's age, which is X, based on the relationships between Laura, Ethan, and Mia's ages. Let me break this down step by step.
First, Laura is 6 years younger than Ethan. So if I know Laura's age, I can find Ethan's age by adding 6. The problem says Laura is 8 year... | Laura is 6 years younger than Ethan. Given that Laura is 8 years old, we can find Ethan's age by adding 6 to Laura's age:
\[
\text{Ethan's age} = \text{Laura's age} + 6 = 8 + 6 = 14
\]
Ethan is 4 years older than Mia. Therefore, Mia's age can be found by subtracting 4 from Ethan's age:
\[
\text{Mia's age} = \text{Et... | 527 | MetaMath-AIME | <think>
Okay, let's see here. The problem is about figuring out Mia's age, which is X, based on the relationships between Laura, Ethan, and Mia's ages. Let me break this down step by step.
First, Laura is 6 years younger than Ethan. So if I know Laura's age, I can find Ethan's age by adding 6. The problem says Laura i... | [
{
"from": "human",
"value": "Laura is 6 years younger than Ethan. Ethan is 4 years older than Mia. Mia is X years old. Laura is 8 years old. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see here. The problem is about figuring out Mia's age, whi... |
The sale was: 'Buy two bicycles at the regular price and get the third bicycle for 8 dollars.' Lucy paid X dollars for three bicycles. The regular price of one bicycle is 80. What is the value of the unknown variable X? | To solve this problem, we need to determine the total cost Lucy paid for three bicycles based on the sale offer.
1. The regular price of one bicycle is given as $80.
2. According to the sale, if Lucy buys two bicycles at the regular price, the third bicycle costs only $8.
Let's calculate the total cost for three bicy... | Okay, so Lucy bought three bicycles, and there's a sale going on: "Buy two at the regular price, get the third for 8 dollars." The regular price of one bicycle is 80 dollars. We need to find out how much Lucy paid in total, which is X.
Hmm, let's break this down. The sale says if you buy two bicycles at the regular pr... | Lucy bought three bicycles under a sale where buying two at the regular price gets the third for 8 dollars. The regular price of one bicycle is 80 dollars.
To calculate the total amount Lucy paid:
1. The cost for two bicycles at the regular price is \( 2 \times 80 = 160 \) dollars.
2. The cost for the third bicycle i... | 512 | MetaMath-AIME | <think>
Okay, so Lucy bought three bicycles, and there's a sale going on: "Buy two at the regular price, get the third for 8 dollars." The regular price of one bicycle is 80 dollars. We need to find out how much Lucy paid in total, which is X.
Hmm, let's break this down. The sale says if you buy two bicycles at the re... | [
{
"from": "human",
"value": "The sale was: 'Buy two bicycles at the regular price and get the third bicycle for 8 dollars.' Lucy paid X dollars for three bicycles. The regular price of one bicycle is 80. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, s... |
During an athletics competition, Team A and Team B scored a total of X points, and Team A won by 22 points. Team B scored 35 points. What is the value of the unknown variable X? | To solve this problem, we need to figure out the total points scored by both teams, which is represented by the variable X.
Let's break down the information given:
1. Team B scored 35 points.
2. Team A won by 22 points.
This means that the score of Team A can be expressed as:
Score of Team A = Score of Team B + 22 =... | Okay, let's see. I need to figure out the total points scored by Team A and Team B, which is X. The problem says that Team A won by 22 points, and Team B scored 35 points. Hmm, let me break this down step by step.
First, Team B's score is given as 35 points. Since Team A won by 22 points, that means Team A's score is ... | Team B scored 35 points, and Team A won by 22 points. Therefore, Team A's score is calculated as follows:
\[
\text{Team A's points} = \text{Team B's points} + 22 = 35 + 22 = 57
\]
The total points \( X \) scored by both teams is the sum of Team A's and Team B's points:
\[
X = \text{Team A's points} + \text{Team B's ... | 17 | MetaMath-AIME | <think>
Okay, let's see. I need to figure out the total points scored by Team A and Team B, which is X. The problem says that Team A won by 22 points, and Team B scored 35 points. Hmm, let me break this down step by step.
First, Team B's score is given as 35 points. Since Team A won by 22 points, that means Team A's s... | [
{
"from": "human",
"value": "During an athletics competition, Team A and Team B scored a total of X points, and Team A won by 22 points. Team B scored 35 points. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. I need to figure out the total p... |
Last spring, there were 60 adult turtles in a conservation center. One-fifth of the turtles were pregnant females. Each pregnant female laid an average of X eggs. The total number of turtles and eggs in the center is 132. What is the value of the unknown variable X? | To solve this problem, we need to determine the value of X, which represents the average number of eggs laid by each pregnant female turtle.
Let's break down the information given:
- The total number of adult turtles in the conservation center is 60.
- One-fifth of the turtles are pregnant females.
- The total number ... | Okay, let's see. I need to find the value of X, which is the average number of eggs each pregnant female turtle laid. The problem says there were 60 adult turtles in the conservation center last spring. Out of these, one-fifth were pregnant females. So first, let me figure out how many pregnant females there were.
One... | Last spring, there were 60 adult turtles in a conservation center. One-fifth of these turtles were pregnant females, which is calculated as follows:
\[
\frac{60}{5} = 12
\]
Each pregnant female laid an average of \( X \) eggs, resulting in a total of \( 12X \) eggs. The problem states that the total number of turtles... | 440 | MetaMath-AIME | <think>
Okay, let's see. I need to find the value of X, which is the average number of eggs each pregnant female turtle laid. The problem says there were 60 adult turtles in the conservation center last spring. Out of these, one-fifth were pregnant females. So first, let me figure out how many pregnant females there we... | [
{
"from": "human",
"value": "Last spring, there were 60 adult turtles in a conservation center. One-fifth of the turtles were pregnant females. Each pregnant female laid an average of X eggs. The total number of turtles and eggs in the center is 132. What is the value of the unknown variable X?"
},
{
... |
During a hiking trip, Alex walks a distance of X miles in 4 hours. What is Alex's average speed in miles per hour? If we know the answer to the above question is 3, what is the value of unknown variable X? | To solve this problem, we need to determine the average speed of Alex during his hiking trip. The average speed is calculated by dividing the distance traveled by the time taken to travel that distance.
We are given the following information:
- Distance traveled: X miles
- Time taken: 4 hours
The formula for average ... | Okay, so Alex went on a hiking trip and walked a distance of X miles in 4 hours. The question is asking for Alex's average speed in miles per hour. Then, if we know that the average speed is 3 miles per hour, we need to find the value of X. Hmm, let's break this down step by step.
First, average speed is generally cal... | To find Alex's average speed, we use the formula for average speed:
\[
\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}
\]
Given that Alex walks \( X \) miles in 4 hours, the average speed is:
\[
\text{Average speed} = \frac{X}{4}
\]
We know the average speed is 3 miles per hour. Setting up th... | 1,150 | MetaMath-AIME | <think>
Okay, so Alex went on a hiking trip and walked a distance of X miles in 4 hours. The question is asking for Alex's average speed in miles per hour. Then, if we know that the average speed is 3 miles per hour, we need to find the value of X. Hmm, let's break this down step by step.
First, average speed is gener... | [
{
"from": "human",
"value": "During a hiking trip, Alex walks a distance of X miles in 4 hours. What is Alex's average speed in miles per hour? If we know the answer to the above question is 3, what is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so Alex went on... |
The value of X + 7^2 is 98. What is the value of the unknown variable X? | To solve for the unknown variable X, we can start by rewriting the equation given in the question:
X + 7^2 = 98
Next, we calculate 7^2:
7^2 = 49
Now substituting this back into the equation gives:
X + 49 = 98
To isolate X, we subtract 49 from both sides:
X + 49 - 49 = 98 - 49
This simplifies to:
X = 49
Thus, the ... | Okay, so I need to find the value of X in the equation X + 7 squared equals 98. Let me break this down step by step. First, the problem says that when you add X and 7 squared together, the result is 98. So, translating that into an equation, it would be X + 7² = 98.
Alright, let me make sure I understand the componen... | To determine the value of \( X \) in the equation \( X + 7^2 = 98 \):
1. **Calculate \( 7^2 \):**
\[
7^2 = 49
\]
2. **Substitute \( 49 \) into the equation:**
\[
X + 49 = 98
\]
3. **Solve for \( X \) by isolating it:**
\[
X = 98 - 49
\]
\[
X = 49
\]
**Verification:**
Substitute \... | 771 | MetaMath-AIME | <think>
Okay, so I need to find the value of X in the equation X + 7 squared equals 98. Let me break this down step by step. First, the problem says that when you add X and 7 squared together, the result is 98. So, translating that into an equation, it would be X + 7² = 98.
Alright, let me make sure I understand the ... | [
{
"from": "human",
"value": " The value of X + 7^2 is 98. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the value of X in the equation X + 7 squared equals 98. Let me break this down step by step. First, the problem says that when yo... |
A regular 20-gon has L lines of symmetry, and the smallest positive angle for which it has rotational symmetry is X degrees. What is L + X? If we know the answer to the above question is 38, what is the value of unknown variable X? | To solve this problem, we first need to determine the number of lines of symmetry (L) and the smallest positive angle for which the regular 20-gon has rotational symmetry (X).
1. **Lines of Symmetry (L)**: For any regular polygon with n sides, the number of lines of symmetry is equal to the number of sides. Therefor... | Okay, so I need to figure out the value of X, which is the smallest positive angle of rotational symmetry for a regular 20-gon. The problem also mentions that L is the number of lines of symmetry, and that L + X equals 38. Since we know the answer is 38, and we need to find X, I guess I have to first recall some proper... | A regular 20-gon has 20 lines of symmetry, so \( L = 20 \). The smallest positive angle for rotational symmetry is calculated by dividing 360 degrees by the number of sides, which gives \( \frac{360}{20} = 18 \) degrees. Therefore, \( X = 18 \).
Given that \( L + X = 38 \), we substitute the known values:
\[
20 + X =... | 1,210 | MetaMath-AIME | <think>
Okay, so I need to figure out the value of X, which is the smallest positive angle of rotational symmetry for a regular 20-gon. The problem also mentions that L is the number of lines of symmetry, and that L + X equals 38. Since we know the answer is 38, and we need to find X, I guess I have to first recall som... | [
{
"from": "human",
"value": "A regular 20-gon has L lines of symmetry, and the smallest positive angle for which it has rotational symmetry is X degrees. What is L + X? If we know the answer to the above question is 38, what is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "<thi... |
A small packet of seeds contains X grams of seeds, while a large packet holds 600 grams. How many small packets should Mia buy to fill one large packet completely? If we know the answer to the above question is 15, what is the value of unknown variable X? | To solve this problem, we need to determine how many small packets of seeds make up the weight of one large packet (600 grams) and then find the weight of each small packet (X grams).
Given that Mia needs to fill 600 grams using small packets that contain X grams each, we set up the following equation:
Number of sma... | Okay, let's see. The problem is about Mia wanting to fill a large packet of seeds using small packets. The large packet holds 600 grams, and each small packet has X grams. We need to find out how many small packets Mia should buy to completely fill one large packet. Then, we're told that the answer is 15, and we need t... | Mia needs to fill a large packet of 600 grams using small packets each containing \( X \) grams. The number of small packets required is given as 15. To find \( X \), we set up the equation:
\[
15 \times X = 600
\]
Solving for \( X \):
\[
X = \frac{600}{15} = 40
\]
Verification: 15 small packets each containing 40 ... | 943 | MetaMath-AIME | <think>
Okay, let's see. The problem is about Mia wanting to fill a large packet of seeds using small packets. The large packet holds 600 grams, and each small packet has X grams. We need to find out how many small packets Mia should buy to completely fill one large packet. Then, we're told that the answer is 15, and w... | [
{
"from": "human",
"value": "A small packet of seeds contains X grams of seeds, while a large packet holds 600 grams. How many small packets should Mia buy to fill one large packet completely? If we know the answer to the above question is 15, what is the value of unknown variable X?"
},
{
"from": "... |
In a school with 600 students, a recent survey indicated that one-third of them prefer soccer while the remaining students prefer basketball. How many students are in favor of soccer? | To find the number of students who prefer soccer, we start by noting that there are a total of 600 students in the school. According to the survey, one-third of these students prefer soccer. We can calculate this as follows:
1. Calculate one-third of the total number of students:
\[ \text{Number of students who pre... | Okay, let's see. The problem is about a school with 600 students. A survey says that one-third prefer soccer, and the rest prefer basketball. We need to find out how many students are in favor of soccer.
Hmm, so first, the total number of students is 600. The key information here is that one-third of them prefer socce... | The total number of students in the school is 600. According to the survey, one-third of them prefer soccer. To find the number of students who prefer soccer, we calculate one-third of 600:
\[
\frac{1}{3} \times 600 = \frac{600}{3} = 200
\]
Thus, the number of students who are in favor of soccer is \boxed{200}. | 370 | MetaMath-AIME | <think>
Okay, let's see. The problem is about a school with 600 students. A survey says that one-third prefer soccer, and the rest prefer basketball. We need to find out how many students are in favor of soccer.
Hmm, so first, the total number of students is 600. The key information here is that one-third of them pref... | [
{
"from": "human",
"value": "In a school with 600 students, a recent survey indicated that one-third of them prefer soccer while the remaining students prefer basketball. How many students are in favor of soccer?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. The problem is about a sch... |
At a bookstore: "Buy 4 novels at the standard price and get the fifth one for 7 dollars." Rachel spent X dollars on five novels. The standard price of one novel was 25. What is the value of the unknown variable X? | To solve this problem, let's first understand the pricing scheme presented. Rachel buys 4 novels at the standard price and gets the fifth one at a discounted price of 7 dollars. We know the standard price of one novel is \$25. Therefore, let's break down the total cost step-by-step.
1. Calculate the total cost of the ... | Okay, let's see. Rachel bought five novels at a bookstore. The deal is "Buy 4 novels at the standard price and get the fifth one for 7 dollars." The standard price of one novel is 25 dollars. We need to find out how much Rachel spent in total, which is X dollars.
First, let me break down the problem. She buys five nov... | Rachel bought five novels at a bookstore where the promotion is "Buy 4 novels at the standard price and get the fifth one for 7 dollars." The standard price of one novel is 25 dollars.
To calculate the total amount Rachel spent, we need to consider the promotion. She buys four novels at the standard price and the fift... | 691 | MetaMath-AIME | <think>
Okay, let's see. Rachel bought five novels at a bookstore. The deal is "Buy 4 novels at the standard price and get the fifth one for 7 dollars." The standard price of one novel is 25 dollars. We need to find out how much Rachel spent in total, which is X dollars.
First, let me break down the problem. She buys ... | [
{
"from": "human",
"value": "At a bookstore: \"Buy 4 novels at the standard price and get the fifth one for 7 dollars.\" Rachel spent X dollars on five novels. The standard price of one novel was 25. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's... |
A miniature version of the Colosseum is created at a scale of $1:200$. The actual height of the Colosseum is X feet. What is the height of the model in feet to the nearest whole number? If we know the answer to the above question is 1, what is the value of unknown variable X? | To solve for the height of the actual Colosseum (X) given the scale of the model, we can set up the relationship between the scale and height. The scale of 1:200 means that 1 unit in the model represents 200 units in reality.
Given that the height of the model is 1 foot, we can set up the equation as follows:
height ... | Okay, let's see here. There's a miniature Colosseum created at a scale of 1:200. The actual height is X feet, and the model's height is 1 foot. I need to find X. Hmm, scales can sometimes be confusing, but I remember that scale models are proportional. So, the ratio of the model to the actual is 1:200. That means 1 uni... | Given a miniature version of the Colosseum created at a scale of \(1:200\), we know the height of the model is 1 foot. We need to find the actual height \(X\) of the Colosseum.
The scale factor \(1:200\) means that 1 unit on the model corresponds to 200 units in real life. Therefore, the actual height \(X\) can be cal... | 455 | MetaMath-AIME | <think>
Okay, let's see here. There's a miniature Colosseum created at a scale of 1:200. The actual height is X feet, and the model's height is 1 foot. I need to find X. Hmm, scales can sometimes be confusing, but I remember that scale models are proportional. So, the ratio of the model to the actual is 1:200. That mea... | [
{
"from": "human",
"value": "A miniature version of the Colosseum is created at a scale of $1:200$. The actual height of the Colosseum is X feet. What is the height of the model in feet to the nearest whole number? If we know the answer to the above question is 1, what is the value of unknown variable X?"
... |
Calculate the sum of the two smallest prime factors of 56. | To find the two smallest prime factors of 56, we first need to factorize 56 into its prime components.\n\nStep 1: Start with the smallest prime number, which is 2. Check if 56 is divisible by 2.\n- 56 ÷ 2 = 28, so 2 is a prime factor.\n\nStep 2: Now, factor 28 further. Check if it's divisible by 2 again.\n- 28 ÷ 2 = 14... | Okay, let's see. I need to find the sum of the two smallest prime factors of 56. Hmm, primes are numbers greater than 1 that have no divisors other than 1 and themselves. So first, I need to factorize 56 into its prime components and then add the two smallest ones. Let me start by breaking down 56.
I know that 56 is a... | To determine the sum of the two smallest prime factors of 56, we start by factorizing the number.
56 is even, so it's divisible by 2:
\[ 56 \div 2 = 28 \]
28 is also even:
\[ 28 \div 2 = 14 \]
14 is even again:
\[ 14 \div 2 = 7 \]
7 is a prime number.
Thus, the prime factors of 56 are \(2\) and \(7\). The two small... | 721 | MetaMath-AIME | <think>
Okay, let's see. I need to find the sum of the two smallest prime factors of 56. Hmm, primes are numbers greater than 1 that have no divisors other than 1 and themselves. So first, I need to factorize 56 into its prime components and then add the two smallest ones. Let me start by breaking down 56.
I know that... | [
{
"from": "human",
"value": "Calculate the sum of the two smallest prime factors of 56."
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. I need to find the sum of the two smallest prime factors of 56. Hmm, primes are numbers greater than 1 that have no divisors other than 1 and themselve... |
Mark uses X pounds of pasta to prepare 12 servings of fettuccine. How many pounds of pasta does he need to prepare 36 servings for a family gathering? If we know the answer to the above question is 12, what is the value of unknown variable X? | To solve this problem, we need to determine the value of X, which represents the pounds of pasta needed to prepare 12 servings of fettuccine.
First, we can find the amount of pasta used per serving by dividing the pounds of pasta (X) by the number of servings (12):
Amount of pasta per serving = X / 12
Now, to find ... | Okay, so Mark uses X pounds of pasta to make 12 servings of fettuccine. The question is asking how many pounds he needs for 36 servings, and they tell us the answer is 12. Then we have to find X. Hmm, let me think.
First, if 12 servings require X pounds, then 36 servings would require more pasta. Since 36 is three tim... | Mark uses \( X \) pounds of pasta to prepare 12 servings of fettuccine. To find how many pounds of pasta are needed for 36 servings, we recognize that 36 servings is three times 12 servings. Therefore, the amount of pasta needed is three times \( X \). Given that the answer for 36 servings is 12 pounds, we set up the e... | 453 | MetaMath-AIME | <think>
Okay, so Mark uses X pounds of pasta to make 12 servings of fettuccine. The question is asking how many pounds he needs for 36 servings, and they tell us the answer is 12. Then we have to find X. Hmm, let me think.
First, if 12 servings require X pounds, then 36 servings would require more pasta. Since 36 is t... | [
{
"from": "human",
"value": "Mark uses X pounds of pasta to prepare 12 servings of fettuccine. How many pounds of pasta does he need to prepare 36 servings for a family gathering? If we know the answer to the above question is 12, what is the value of unknown variable X?"
},
{
"from": "gpt",
"va... |
The chart shows the distances run by athletes Sam and Jake after 2 hours. If Sam ran 50 miles and Jake ran X miles, how many more miles did Sam run than Jake? If we know the answer to the above question is 20, what is the value of unknown variable X? | To solve this problem, we need to find the value of X, which represents the number of miles Jake ran. We are given that Sam ran 50 miles and the difference in the distance run between Sam and Jake is 20 miles.
Let's set up the equation based on the information given:
Distance run by Sam - Distance run by Jake = 20 m... | Okay, let me try to figure this out. So, the problem says that there's a chart showing the distances run by Sam and Jake after 2 hours. Sam ran 50 miles, and Jake ran X miles. The question is asking how many more miles Sam ran than Jake, and we know the answer to that is 20. We need to find the value of X.
Alright, le... | The difference in distances run by Sam and Jake is given as 20 miles. Since Sam ran 50 miles and Jake ran \( X \) miles, we set up the equation:
\[
50 - X = 20
\]
Solving for \( X \):
\[
X = 50 - 20 = 30
\]
**Answer:** The value of \( X \) is \(\boxed{30}\). | 134 | MetaMath-AIME | <think>
Okay, let me try to figure this out. So, the problem says that there's a chart showing the distances run by Sam and Jake after 2 hours. Sam ran 50 miles, and Jake ran X miles. The question is asking how many more miles Sam ran than Jake, and we know the answer to that is 20. We need to find the value of X.
Alr... | [
{
"from": "human",
"value": "The chart shows the distances run by athletes Sam and Jake after 2 hours. If Sam ran 50 miles and Jake ran X miles, how many more miles did Sam run than Jake? If we know the answer to the above question is 20, what is the value of unknown variable X?"
},
{
"from": "gpt",... |
In a factory with a total of 240 workers, if 25% of them are technicians, what is the number of workers who are not technicians? | To find the number of workers who are not technicians, we first need to determine how many technicians there are in the factory.
1. Calculate 25% of the total number of workers:
- 25% of 240 workers = \(0.25 \times 240 = 60\) technicians.
2. Next, to find the number of workers who are not technicians, subtract th... | Okay, let's see. There's this factory with 240 workers total. The question is asking how many of them are not technicians, given that 25% are technicians. Hmm, okay. So first, I need to find out how many technicians there are, and then subtract that number from the total number of workers to get the ones who aren't tec... | To find the number of workers who are not technicians in a factory with 240 workers, where 25% are technicians:
1. Calculate the number of technicians:
\[
25\% \text{ of } 240 = 0.25 \times 240 = 60
\]
2. Subtract the number of technicians from the total number of workers:
\[
240 - 60 = 180
\]
Alter... | 504 | MetaMath-AIME | <think>
Okay, let's see. There's this factory with 240 workers total. The question is asking how many of them are not technicians, given that 25% are technicians. Hmm, okay. So first, I need to find out how many technicians there are, and then subtract that number from the total number of workers to get the ones who ar... | [
{
"from": "human",
"value": "In a factory with a total of 240 workers, if 25% of them are technicians, what is the number of workers who are not technicians?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. There's this factory with 240 workers total. The question is asking how many of t... |
Emma's technical school has X times as many students as Noah's technical school. The total enrollment at both schools is 8400. How many students does Emma's technical school have? If we know the answer to the above question is 7200, what is the value of unknown variable X? | To solve the problem, we need to determine the value of X, which represents the ratio of the number of students at Emma's technical school to the number of students at Noah's technical school.
Let's denote the number of students at Noah's school as N. According to the problem:
- The number of students at Emma's school... | Okay, let's see. I need to find the value of X, which represents how many times as many students Emma's technical school has compared to Noah's. The total enrollment is 8400, and we know the answer for Emma's school is 7200. Hmm, okay.
First, let me set up the problem. Let's denote the number of students at Noah's sch... | Let \( N \) be the number of students at Noah's technical school. Emma's technical school has \( X \) times as many students as Noah's, so the number of students at Emma's school is \( X \cdot N \). The total enrollment at both schools is 8400, which gives us the equation:
\[
N + X \cdot N = 8400
\]
We know the numbe... | 98 | MetaMath-AIME | <think>
Okay, let's see. I need to find the value of X, which represents how many times as many students Emma's technical school has compared to Noah's. The total enrollment is 8400, and we know the answer for Emma's school is 7200. Hmm, okay.
First, let me set up the problem. Let's denote the number of students at No... | [
{
"from": "human",
"value": "Emma's technical school has X times as many students as Noah's technical school. The total enrollment at both schools is 8400. How many students does Emma's technical school have? If we know the answer to the above question is 7200, what is the value of unknown variable X?"
},... |
Kevin had enough paint for X square feet of wall space. After losing 6 cans on the way, he can now paint only 54 square feet. He needed 54 cans to paint the 54 square feet. What is the value of the unknown variable X? | To solve this problem, we need to break down the information given and set up an equation to find the unknown variable X.
1. Kevin had enough paint for X square feet of wall space initially.
2. He loses 6 cans of paint, and after this loss, he can paint only 54 square feet.
3. It is stated that to paint 54 square feet... | Okay, let's see here. So Kevin had enough paint for X square feet of wall space. But then he lost 6 cans on the way, and now he can only paint 54 square feet. They also mention that he needed 54 cans to paint those 54 square feet. The question is asking for the value of X.
Hmm, let me break this down. Initially, Kevi... | Kevin initially had enough paint for \( X \) square feet of wall space. After losing 6 cans, he could only paint 54 square feet, which required 54 cans. This implies that each can of paint covers 1 square foot (since 54 cans are needed for 54 square feet).
Let \( X \) be the initial number of cans Kevin had. After los... | 564 | MetaMath-AIME | <think>
Okay, let's see here. So Kevin had enough paint for X square feet of wall space. But then he lost 6 cans on the way, and now he can only paint 54 square feet. They also mention that he needed 54 cans to paint those 54 square feet. The question is asking for the value of X.
Hmm, let me break this down. Initial... | [
{
"from": "human",
"value": "Kevin had enough paint for X square feet of wall space. After losing 6 cans on the way, he can now paint only 54 square feet. He needed 54 cans to paint the 54 square feet. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let... |
If William has $45, and Jessica has $3 more than Emma, while Emma has half the amount of William, how much money does Jessica possess? | 1. We know that William has $45.
2. The problem states that Emma has half the amount of William. Therefore, Emma has:
\[ \text{Emma's amount} = \frac{45}{2} = 22.5 \text{ dollars} \]
3. The problem also states that Jessica has $3 more than Emma. So Jessica has:
\[ \text{Jessica's amount} = 22.5 + 3 = 25.5 \... | Okay, let's see. So the problem is: William has $45, Jessica has $3 more than Emma, and Emma has half the amount of William. We need to find out how much money Jessica has. Hmm, let me break this down step by step.
First, let's list out the information given. William has $45. That's straightforward. Then, Emma has hal... | William has $45. Emma has half the amount of William, which is calculated as follows:
\[
\text{Emma's amount} = \frac{45}{2} = 22.5
\]
Jessica has $3 more than Emma. Therefore, Jessica's amount is:
\[
\text{Jessica's amount} = 22.5 + 3 = 25.5
\]
Thus, the final answer is:
\[
\boxed{25.50}
\] | 1,046 | MetaMath-AIME | <think>
Okay, let's see. So the problem is: William has $45, Jessica has $3 more than Emma, and Emma has half the amount of William. We need to find out how much money Jessica has. Hmm, let me break this down step by step.
First, let's list out the information given. William has $45. That's straightforward. Then, Emma... | [
{
"from": "human",
"value": "If William has $45, and Jessica has $3 more than Emma, while Emma has half the amount of William, how much money does Jessica possess?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. So the problem is: William has $45, Jessica has $3 more than Emma, and Emma... |
Sarah bought ten erasers for $0.80 each. The next day, a 5%-off sale occurred. How much could Sarah have saved by waiting X day? If we know the answer to the above question is 0.40, what is the value of unknown variable X? | To solve this problem, we need to determine how much Sarah could have saved by waiting for the 5%-off sale on the erasers she bought earlier. Let's break down the information provided step by step:
1. **Original Price of Erasers:** Sarah bought ten erasers for $0.80 each.
Total cost of ten erasers = 10 * $0.80 ... | Okay, let's see. Sarah bought ten erasers for $0.80 each. So first, I need to figure out how much she spent. Then, the next day, there was a 5%-off sale. The question is asking how much she could have saved by waiting X days. And they told us the answer is $0.40, so we need to find X. Hmm, wait, but the problem says "t... | Sarah bought ten erasers for $0.80 each. The total cost without any discount is calculated as follows:
\[
10 \times 0.80 = 8.00 \text{ dollars}
\]
The next day, a 5%-off sale occurred. The discounted price per eraser is:
\[
0.80 - (0.05 \times 0.80) = 0.80 - 0.04 = 0.76 \text{ dollars}
\]
The total cost for ten erase... | 418 | MetaMath-AIME | <think>
Okay, let's see. Sarah bought ten erasers for $0.80 each. So first, I need to figure out how much she spent. Then, the next day, there was a 5%-off sale. The question is asking how much she could have saved by waiting X days. And they told us the answer is $0.40, so we need to find X. Hmm, wait, but the problem... | [
{
"from": "human",
"value": "Sarah bought ten erasers for $0.80 each. The next day, a 5%-off sale occurred. How much could Sarah have saved by waiting X day? If we know the answer to the above question is 0.40, what is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay... |
At the beginning of the academic year, Mark aimed to achieve an A in at least 78% of his total 80 quizzes. Having earned an A on 45 out of the 50 quizzes completed so far, what is the maximum number of remaining quizzes on which he can score less than an A? | 1. Calculate how many A's Mark needs to achieve his goal:
To have an A in at least 78% of 80 quizzes, he needs to have A's in:
\[ 0.78 \times 80 = 62.4 \text{ (round up to 63)} \]
Thus, he needs at least 63 A's.
2. Determine how many A's he has already:
Mark has already scored A's on 45 quizzes.
3. Ca... | Okay, so Mark wants to get an A in at least 78% of his total 80 quizzes. Let me break that down. First, I need to find out how many quizzes he needs to get an A in to meet his goal.
78% of 80 quizzes is... let me calculate that. 0.78 times 80. Hmm, 0.78*80. Well, 0.7*80 is 56, and 0.08*80 is 6.4, so adding those toge... | Mark aims to achieve an A in at least 78% of his total 80 quizzes. To find out how many A's he needs, we calculate 78% of 80:
\[
0.78 \times 80 = 62.4
\]
Since he can't have a fraction of a quiz, he needs at least 63 A's. Mark has already earned 45 A's out of 50 completed quizzes. Therefore, he needs:
\[
63 - 45 = 1... | 1,249 | MetaMath-AIME | <think>
Okay, so Mark wants to get an A in at least 78% of his total 80 quizzes. Let me break that down. First, I need to find out how many quizzes he needs to get an A in to meet his goal.
78% of 80 quizzes is... let me calculate that. 0.78 times 80. Hmm, 0.78*80. Well, 0.7*80 is 56, and 0.08*80 is 6.4, so adding th... | [
{
"from": "human",
"value": "At the beginning of the academic year, Mark aimed to achieve an A in at least 78% of his total 80 quizzes. Having earned an A on 45 out of the 50 quizzes completed so far, what is the maximum number of remaining quizzes on which he can score less than an A?"
},
{
"from":... |
Four equidistant fences are installed along a field. The distance between the first fence and the third fence is X meters. How far apart are the first and last fences? If we know the answer to the above question is 54, what is the value of unknown variable X? | To solve this problem, we need to understand the arrangement of the fences and how they are spaced. We have four equidistant fences, which means they are equally spaced apart from each other.
Let’s denote the distance between each consecutive fence as \(d\) meters.
- The first fence is at position 0 meters.
- The sec... | Okay, let me try to figure out this problem. So, there are four equidistant fences installed along a field. The distance between the first fence and the third fence is X meters. We need to find how far apart the first and last fences are, and if the answer is 54, we have to find X. Hmm, let me break this down step by s... | The four equidistant fences create three equal intervals between them. Let the distance between each consecutive fence be \( d \) meters.
The distance from the first to the third fence spans two intervals, so \( X = 2d \). The distance from the first to the last (fourth) fence spans three intervals, which is given as... | 889 | MetaMath-AIME | <think>
Okay, let me try to figure out this problem. So, there are four equidistant fences installed along a field. The distance between the first fence and the third fence is X meters. We need to find how far apart the first and last fences are, and if the answer is 54, we have to find X. Hmm, let me break this down s... | [
{
"from": "human",
"value": "Four equidistant fences are installed along a field. The distance between the first fence and the third fence is X meters. How far apart are the first and last fences? If we know the answer to the above question is 54, what is the value of unknown variable X?"
},
{
"from... |
Lily's family ordered a 14-slice pizza for lunch. Lily ate two slices and shared X slices equally with her friend Zoe. What fraction of the pizza did Lily eat? If we know the answer to the above question is 3/14, what is the value of unknown variable X? | To find the value of X, we need to determine how many slices Lily ate in total and then express that as a fraction of the whole pizza.
1. Total slices in the pizza: 14 slices
2. Slices Lily ate: 2 slices
3. Slices shared with Zoe: X slices
4. Total slices Lily had: 2 + (X/2) (since they share the X slices equally)
T... | Alright, let's tackle this pizza problem step by step. So, Lily's family ordered a 14-slice pizza. Lily ate two slices herself and then shared some number of slices, X, equally with her friend Zoe. We need to figure out what fraction of the pizza Lily ate, and then determine the value of X given that the fraction is 3/... | Lily ate 2 slices by herself and shared \( X \) slices equally with Zoe, meaning she ate \( \frac{X}{2} \) additional slices. The total number of slices she ate is \( 2 + \frac{X}{2} \). Given the total pizza has 14 slices, the fraction Lily ate is:
\[
\frac{2 + \frac{X}{2}}{14} = \frac{3}{14}
\]
Solving for \( X \):... | 649 | MetaMath-AIME | <think>
Alright, let's tackle this pizza problem step by step. So, Lily's family ordered a 14-slice pizza. Lily ate two slices herself and then shared some number of slices, X, equally with her friend Zoe. We need to figure out what fraction of the pizza Lily ate, and then determine the value of X given that the fracti... | [
{
"from": "human",
"value": "Lily's family ordered a 14-slice pizza for lunch. Lily ate two slices and shared X slices equally with her friend Zoe. What fraction of the pizza did Lily eat? If we know the answer to the above question is 3/14, what is the value of unknown variable X?"
},
{
"from": "gp... |
In the spring of last year, a conservation center housed 60 adult turtles, with one-fifth of them being pregnant females. Each pregnant female laid approximately 6 eggs. What is the total number of turtles and eggs combined in the center? | 1. **Identify the number of pregnant females:****
There are a total of 60 adult turtles, and one-fifth of them are pregnant females.
\[ \text{Number of pregnant females} = \frac{1}{5} \times 60 = 12 \text{ females} \]
2. **Calculate the total number of eggs laid:**
Each pregnant female lays approxi... | Okay, let's see here. The problem is about a conservation center that had 60 adult turtles last spring, and one-fifth of them were pregnant females. Each of those pregnant females laid around 6 eggs. The question is asking for the total number of turtles and eggs combined in the center. Hmm, so I need to calculate the ... | The conservation center had 60 adult turtles, with \( \frac{1}{5} \) of them being pregnant females:
\[ \frac{60}{5} = 12 \text{ pregnant females} \]
Each pregnant female laid 6 eggs, so the total number of eggs is:
\[ 12 \times 6 = 72 \text{ eggs} \]
Combining the original 60 turtles with the 72 eggs gives: ... | 875 | MetaMath-AIME | <think>
Okay, let's see here. The problem is about a conservation center that had 60 adult turtles last spring, and one-fifth of them were pregnant females. Each of those pregnant females laid around 6 eggs. The question is asking for the total number of turtles and eggs combined in the center. Hmm, so I need to calcul... | [
{
"from": "human",
"value": "In the spring of last year, a conservation center housed 60 adult turtles, with one-fifth of them being pregnant females. Each pregnant female laid approximately 6 eggs. What is the total number of turtles and eggs combined in the center?"
},
{
"from": "gpt",
"value"... |
If an internet service plan costs $25 per month and charges an additional $1 for every gigabyte used beyond 100 gigabytes, how much will John have to pay in total for April if he used 150 gigabytes of data? | 1. The base cost of the internet service plan is $25 per month.
2. The plan includes 100 gigabytes of data. Since John used 150 gigabytes, he exceeded this limit by:
`150 GB - 100 GB = 50 GB`
3. For every gigabyte over 100 GB, there is an additional charge of $1. Therefore, the extra cost for using 50 gigabyte... | Okay, let's see. John has an internet service plan that costs $25 per month. But there's a catch: if he uses more than 100 gigabytes of data, they charge an extra $1 for every gigabyte over that limit. He used 150 gigabytes in April. So, I need to figure out how much he has to pay in total for that month.
First, the b... | John's internet plan has a base cost of $25 for up to 100 gigabytes. Since he used 150 gigabytes, he exceeded the limit by 50 gigabytes. The overage charge is calculated as 50 gigabytes × $1 per gigabyte = $50. Adding this to the base cost:
**Total Payment = Base Cost + Overage Charge = $25 + $50 = $75**
**Answer:** ... | 750 | MetaMath-AIME | <think>
Okay, let's see. John has an internet service plan that costs $25 per month. But there's a catch: if he uses more than 100 gigabytes of data, they charge an extra $1 for every gigabyte over that limit. He used 150 gigabytes in April. So, I need to figure out how much he has to pay in total for that month.
Firs... | [
{
"from": "human",
"value": "If an internet service plan costs $25 per month and charges an additional $1 for every gigabyte used beyond 100 gigabytes, how much will John have to pay in total for April if he used 150 gigabytes of data?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. Joh... |
Carlos uses X pounds of beef to make 25 tacos. How many pounds of beef will he need to make 75 tacos for a local gathering? If we know the answer to the above question is 30, what is the value of unknown variable X? | To determine the value of X, we first need to find the amount of beef Carlos uses per taco.
Carlos uses X pounds of beef to make 25 tacos. Therefore, the amount of beef per taco is:
\[ \text{Beef per taco} = \frac{X}{25} \text{ pounds} \]
Now, we want to find out how many pounds of beef he will need for 75 tacos. Us... | Okay, let's see. Carlos uses X pounds of beef to make 25 tacos. The question is asking how many pounds he'll need to make 75 tacos, and we're told the answer is 30. We need to find X. Hmm, so I need to figure out what X is, given that 75 tacos require 30 pounds of beef. Let me think step by step.
First, this seems lik... | Carlos uses \( X \) pounds of beef to make 25 tacos. To determine how many pounds of beef he needs to make 75 tacos, we recognize that 75 tacos are three times 25 tacos. Therefore, the amount of beef needed should also be three times as much. Given that 75 tacos require 30 pounds of beef, we can set up the following pr... | 93 | MetaMath-AIME | <think>
Okay, let's see. Carlos uses X pounds of beef to make 25 tacos. The question is asking how many pounds he'll need to make 75 tacos, and we're told the answer is 30. We need to find X. Hmm, so I need to figure out what X is, given that 75 tacos require 30 pounds of beef. Let me think step by step.
First, this s... | [
{
"from": "human",
"value": "Carlos uses X pounds of beef to make 25 tacos. How many pounds of beef will he need to make 75 tacos for a local gathering? If we know the answer to the above question is 30, what is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's... |
Jake has collected X dimes, one nickel, and three pennies. He possesses 48 percent of one dollar with his coins. What is the value of the unknown variable X? | To solve this problem, we need to determine the value of X, which represents the number of dimes Jake collected.
Let's break down the information given:
- Jake has collected X dimes.
- He has 1 nickel.
- He has 3 pennies.
- Jake possesses 48 percent of one dollar.
First, let's express what Jake has in terms of cents:... | Okay, let's see. Jake has some coins: X dimes, one nickel, and three pennies. The total value of these coins is 48 percent of one dollar. I need to find out what X is. Hmm, let's break this down step by step.
First, I should remember the values of each coin. A dime is worth 10 cents, a nickel is 5 cents, and a penny i... | Jake has collected \( X \) dimes, one nickel, and three pennies. The total value of these coins is 48 percent of one dollar.
First, we convert the percentage to cents: 48% of one dollar is \( 0.48 \times 100 = 48 \) cents.
Next, we calculate the total value of Jake's coins. The value of \( X \) dimes is \( 10X \) ce... | 1,270 | MetaMath-AIME | <think>
Okay, let's see. Jake has some coins: X dimes, one nickel, and three pennies. The total value of these coins is 48 percent of one dollar. I need to find out what X is. Hmm, let's break this down step by step.
First, I should remember the values of each coin. A dime is worth 10 cents, a nickel is 5 cents, and a... | [
{
"from": "human",
"value": "Jake has collected X dimes, one nickel, and three pennies. He possesses 48 percent of one dollar with his coins. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. Jake has some coins: X dimes, one nickel, and three ... |
A person jogs for 1 hour at 7 mph and then walks for X minutes at 2 mph. They travel a total of 8 units. What is the value of the unknown variable X? | To solve this problem, we start by calculating the distance covered during the jog.
1. **Jogging Distance**: The person jogs for 1 hour at a speed of 7 mph.
\[ \text{Distance} = \text{Speed} \times \text{Time} = 7 \text{ mph} \times 1 \text{ hour} = 7 \text{ miles} \]
2. **Total Distance**: The total distance tr... | Okay, so I need to figure out how long the person walked at 2 mph such that the total distance they covered is 8 units. Wait, the problem says "units" but mentions miles per hour. Hmm, maybe that's a typo? Because if they're jogging at 7 mph and walking at 2 mph, the total distance should be in miles, right? So maybe t... | The person jogs for 1 hour at 7 mph, covering a distance of:
\[ 7 \, \text{mph} \times 1 \, \text{hour} = 7 \, \text{miles} \]
The person then walks for \( X \) minutes at 2 mph. Converting \( X \) minutes to hours:
\[ X \, \text{minutes} = \frac{X}{60} \, \text{hours} \]
The distance walked is:
\[ 2 \, \text{mph} \t... | 427 | MetaMath-AIME | <think>
Okay, so I need to figure out how long the person walked at 2 mph such that the total distance they covered is 8 units. Wait, the problem says "units" but mentions miles per hour. Hmm, maybe that's a typo? Because if they're jogging at 7 mph and walking at 2 mph, the total distance should be in miles, right? So... | [
{
"from": "human",
"value": "A person jogs for 1 hour at 7 mph and then walks for X minutes at 2 mph. They travel a total of 8 units. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out how long the person walked at 2 mph such that t... |
A cyclist covering a distance of 30 miles spends X hours to finish. The cyclist's average speed is 20 miles per hour. What is the value of the unknown variable X? | To solve this problem, we need to determine the value of X, which represents the time taken by the cyclist to cover 30 miles at an average speed of 20 miles per hour.
We can use the formula for average speed, which is defined as:
\[ \text{Average Speed} = \frac{\text{Distance}}{\text{Time}} \]
Rearranging this formul... | Okay, so I need to figure out how long it took the cyclist to cover 30 miles if their average speed was 20 miles per hour. Hmm, let's start by recalling the basic formula that relates distance, speed, and time. I think it's something like distance equals speed multiplied by time. Let me write that down to be sure: Dist... | To determine the time \( X \) it takes for a cyclist to cover 30 miles at an average speed of 20 miles per hour, we use the formula relating distance, speed, and time:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
Given the distance is 30 miles and the speed is 20 miles per hour, we substitute these values... | 170 | MetaMath-AIME | <think>
Okay, so I need to figure out how long it took the cyclist to cover 30 miles if their average speed was 20 miles per hour. Hmm, let's start by recalling the basic formula that relates distance, speed, and time. I think it's something like distance equals speed multiplied by time. Let me write that down to be su... | [
{
"from": "human",
"value": "A cyclist covering a distance of 30 miles spends X hours to finish. The cyclist's average speed is 20 miles per hour. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out how long it took the cyclist to co... |
A pet adoption center has X pets and wants to match each pet with its new owner. The probability that each owner gets their matched pet when the center randomly assigns pets is 1/362880. What is the value of the unknown variable X? | To solve the problem, we need to determine the value of X, which represents the number of pets at the adoption center.
The probability that each owner gets their matched pet when the center randomly assigns pets is given as 1/362880. This probability can be related to the number of ways to arrange X pets, which is eq... | Okay, let's see. So, there's this pet adoption center with X pets, and they want to match each pet with its new owner. The probability that each owner gets their matched pet when they randomly assign the pets is given as 1/362880. I need to find X.
Hmm, probability of everyone getting their matched pet... That sounds ... | The probability that each owner gets their matched pet when the center randomly assigns pets is given as \( \frac{1}{362880} \). This probability is equivalent to \( \frac{1}{X!} \), where \( X \) is the number of pets. Therefore, we need to find \( X \) such that \( X! = 362880 \).
Calculating factorials step-by-step... | 1,079 | MetaMath-AIME | <think>
Okay, let's see. So, there's this pet adoption center with X pets, and they want to match each pet with its new owner. The probability that each owner gets their matched pet when they randomly assign the pets is given as 1/362880. I need to find X.
Hmm, probability of everyone getting their matched pet... That... | [
{
"from": "human",
"value": "A pet adoption center has X pets and wants to match each pet with its new owner. The probability that each owner gets their matched pet when the center randomly assigns pets is 1/362880. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<thi... |
In an animal shelter, the ratio of dogs to cats is 3:4. Given that there are 70 pets in total at the shelter, how many more cats than dogs are there? | Let's denote the number of dogs as \(3x\) and the number of cats as \(4x\) where \(x\) is a common factor. \n\nFrom the problem, we know that the total number of pets (dogs + cats) is 70: \n\[ 3x + 4x = 70 \] \n\[ 7x = 70 \] \n\[ x = 10 \] \n\nNow we can find the number of dogs and cats: \n\[ \text{Number of Dogs} = 3x... | Okay, let's see. The problem says the ratio of dogs to cats is 3:4, and there are 70 pets in total. We need to find how many more cats there are than dogs. Hmm, ratios can sometimes trip me up, but let's break it down step by step.
First, ratios compare parts to parts. So, dogs are 3 parts and cats are 4 parts. Togeth... | The ratio of dogs to cats is 3:4, meaning for every 3 parts of dogs, there are 4 parts of cats. The total number of parts is \(3 + 4 = 7\).
Given that there are 70 pets in total, each part represents \(\frac{70}{7} = 10\) pets.
- The number of dogs is \(3 \times 10 = 30\).
- The number of cats is \(4 \times 10 = 40... | 725 | MetaMath-AIME | <think>
Okay, let's see. The problem says the ratio of dogs to cats is 3:4, and there are 70 pets in total. We need to find how many more cats there are than dogs. Hmm, ratios can sometimes trip me up, but let's break it down step by step.
First, ratios compare parts to parts. So, dogs are 3 parts and cats are 4 parts... | [
{
"from": "human",
"value": "In an animal shelter, the ratio of dogs to cats is 3:4. Given that there are 70 pets in total at the shelter, how many more cats than dogs are there?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. The problem says the ratio of dogs to cats is 3:4, and there... |
Sally and Greg are cycling to a park that is 5 miles away. Sally cycles at a speed of X miles per hour and Greg at a speed of 10 miles per hour. How many minutes before Greg does Sally arrive? If we know the answer to the above question is 10, what is the value of unknown variable X? | To determine the value of X, we need to find the time taken for both Sally and Greg to reach the park and then calculate how much earlier Sally arrives compared to Greg.
1. **Determine the time taken by Greg:**
Greg cycles at a speed of 10 miles per hour to cover a distance of 5 miles.
Time taken by Greg = D... | Okay, let's see. The problem is about Sally and Greg cycling to a park that's 5 miles away. Sally's speed is X miles per hour, and Greg's speed is 10 miles per hour. We need to find the value of X if Sally arrives 10 minutes before Greg. The answer is given as 10 minutes, so we need to work backwards to find X. Hmm, le... | Sally and Greg are cycling to a park that is 5 miles away. Greg cycles at 10 miles per hour, while Sally cycles at \( X \) miles per hour. We need to find the value of \( X \) such that Sally arrives 10 minutes before Greg.
First, we calculate the time it takes Greg to reach the park:
\[
\text{Time}_{\text{Greg}} = \f... | 862 | MetaMath-AIME | <think>
Okay, let's see. The problem is about Sally and Greg cycling to a park that's 5 miles away. Sally's speed is X miles per hour, and Greg's speed is 10 miles per hour. We need to find the value of X if Sally arrives 10 minutes before Greg. The answer is given as 10 minutes, so we need to work backwards to find X.... | [
{
"from": "human",
"value": "Sally and Greg are cycling to a park that is 5 miles away. Sally cycles at a speed of X miles per hour and Greg at a speed of 10 miles per hour. How many minutes before Greg does Sally arrive? If we know the answer to the above question is 10, what is the value of unknown variab... |
As part of a weekend project, Alice observed a dog and a raccoon bury bones. The dog buried 4 bones in each of the holes it dug, while the raccoon buried 5 bones per hole. Both animals buried the same total number of bones, but the raccoon dug 2 fewer holes than the dog. How many bones did the dog end up burying? | Let's denote the number of holes dug by the dog as \(d\) and the number of holes dug by the raccoon as \(r\). According to the problem, we know the following:
1. The dog buries 4 bones in each hole, hence the total number of bones buried by the dog is \(4d\).
2. The raccoon buries 5 bones in each hole, so the total nu... | Okay, let's see. So Alice watched a dog and a raccoon burying bones. The dog buried 4 bones in each hole, and the raccoon buried 5 bones per hole. Both of them buried the same total number of bones. But the raccoon dug 2 fewer holes than the dog. The question is asking how many bones the dog ended up burying.
Hmm. Alr... | Let \( D \) be the number of holes the dog dug. The raccoon dug \( D - 2 \) holes. The total number of bones buried by the dog is \( 4D \) and by the raccoon is \( 5(D - 2) \). Since they buried the same total number of bones, we set up the equation:
\[
4D = 5(D - 2)
\]
Expanding and solving for \( D \):
\[
4D = 5D ... | 584 | MetaMath-AIME | <think>
Okay, let's see. So Alice watched a dog and a raccoon burying bones. The dog buried 4 bones in each hole, and the raccoon buried 5 bones per hole. Both of them buried the same total number of bones. But the raccoon dug 2 fewer holes than the dog. The question is asking how many bones the dog ended up burying.
... | [
{
"from": "human",
"value": "As part of a weekend project, Alice observed a dog and a raccoon bury bones. The dog buried 4 bones in each of the holes it dug, while the raccoon buried 5 bones per hole. Both animals buried the same total number of bones, but the raccoon dug 2 fewer holes than the dog. How man... |
Mr. Smith measures his square garden and finds it is 10 steps per side. Each of Mr. Smith's steps is 4 feet long. He expects to harvest X pounds of lettuce per square foot from his garden. Mr. Smith expects to harvest 640 pounds of lettuce. What is the value of the unknown variable X? | To solve this problem, we need to determine the value of X, which represents the expected harvest of lettuce in pounds per square foot from Mr. Smith's garden.
Let's break down the information given:
1. Mr. Smith's garden is a square measuring 10 steps on each side.
2. Each of Mr. Smith's steps is 4 feet long. ... | Okay, so Mr. Smith has a square garden, and each side is 10 steps long. Each step he takes is 4 feet. He wants to harvest lettuce, and he expects to get X pounds per square foot. The total he expects is 640 pounds. I need to find X. Let me think step by step.
First, the garden is square, so the area would be side leng... | Mr. Smith's garden is a square with each side measuring 10 steps. Each step is 4 feet long, so the length of one side in feet is:
\[
10 \text{ steps} \times 4 \text{ feet/step} = 40 \text{ feet}
\]
The area of the square garden is:
\[
40 \text{ feet} \times 40 \text{ feet} = 1600 \text{ square feet}
\]
Mr. Smith expe... | 45 | MetaMath-AIME | <think>
Okay, so Mr. Smith has a square garden, and each side is 10 steps long. Each step he takes is 4 feet. He wants to harvest lettuce, and he expects to get X pounds per square foot. The total he expects is 640 pounds. I need to find X. Let me think step by step.
First, the garden is square, so the area would be s... | [
{
"from": "human",
"value": "Mr. Smith measures his square garden and finds it is 10 steps per side. Each of Mr. Smith's steps is 4 feet long. He expects to harvest X pounds of lettuce per square foot from his garden. Mr. Smith expects to harvest 640 pounds of lettuce. What is the value of the unknown varia... |
A school can enroll X new students each month. How many students can it enroll in a year? If we know the answer to the above question is 3600, what is the value of unknown variable X? | To solve this problem, we need to determine the monthly enrollment rate of students, represented by the variable X, given that the total enrollment over a year is 3600 students.
1. We know that there are 12 months in a year.
2. The total number of students that can be enrolled in a year can be expressed as:
Total ... | Okay, let me try to figure out this problem. So, the question says that a school can enroll X new students each month. Then they ask, how many students can it enroll in a year? And if the answer to that is 3600, what is X?
Hmm, alright. Let's start with the first part. If the school enrolls X students every month, the... | The school can enroll \( X \) new students each month. To find the total number of students enrolled in a year, we multiply the monthly enrollment by the number of months in a year, which is 12. Therefore, the total number of students enrolled in a year is \( 12X \).
Given that the total number of students enrolled in... | 1,009 | MetaMath-AIME | <think>
Okay, let me try to figure out this problem. So, the question says that a school can enroll X new students each month. Then they ask, how many students can it enroll in a year? And if the answer to that is 3600, what is X?
Hmm, alright. Let's start with the first part. If the school enrolls X students every mo... | [
{
"from": "human",
"value": "A school can enroll X new students each month. How many students can it enroll in a year? If we know the answer to the above question is 3600, what is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let me try to figure out this problem... |
What is the total of the two smallest prime factors of 84? | To find the total of the two smallest prime factors of 84, we start by determining the prime factorization of 84.
1. **Divide by the smallest prime**: The smallest prime number is 2.\
Dividing 84 by 2 gives us: \ \ \ \ \ 84 ÷ 2 = 42
2. **Continue with 2**: Now, we divide 42 by 2 again: \ \ \ \ \ 42 ÷ 2 = 21\
(... | Okay, so I need to find the total of the two smallest prime factors of 84. Hmm, let's start by recalling what prime factors are. Prime factors are the prime numbers that multiply together to give the original number, which in this case is 84.
First, maybe I should break down 84 into its prime factors. Let me try divi... | To find the total of the two smallest prime factors of 84, we start by breaking down 84 into its prime factors.
1. Divide 84 by the smallest prime number, 2:
\[
84 \div 2 = 42
\]
Continue dividing by 2:
\[
42 \div 2 = 21
\]
So, 2 is a prime factor.
2. Next, divide 21 by the next smallest prim... | 588 | MetaMath-AIME | <think>
Okay, so I need to find the total of the two smallest prime factors of 84. Hmm, let's start by recalling what prime factors are. Prime factors are the prime numbers that multiply together to give the original number, which in this case is 84.
First, maybe I should break down 84 into its prime factors. Let me ... | [
{
"from": "human",
"value": "What is the total of the two smallest prime factors of 84?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the total of the two smallest prime factors of 84. Hmm, let's start by recalling what prime factors are. Prime factors are the prime numbers tha... |
In a community with 350 members, each person is part of either a book club, a film club, or both. Given that 210 members are in the book club and 180 members are in the film club, how many members are exclusively in the film club? | We will use the principle of inclusion-exclusion to solve this problem. Let \( A \) be the set of members in the book club and \( B \) be the set of members in the film club. We know from the problem statement:
1. The total number of members in the community is 350.
2. The number of members in the book club, \|A\|, is... | Okay, so I need to figure out how many people are exclusively in the film club. The community has 350 members, and everyone is in either the book club, the film club, or both. The book club has 210 members, and the film club has 180. Hmm, let's start by recalling some set theory basics.
Since people can be in both clu... | Given a community with 350 members where each person is part of either a book club, a film club, or both, we need to determine the number of members exclusively in the film club.
We know:
- The book club has 210 members.
- The film club has 180 members.
Using the principle of inclusion-exclusion, we calculate the nu... | 52 | MetaMath-AIME | <think>
Okay, so I need to figure out how many people are exclusively in the film club. The community has 350 members, and everyone is in either the book club, the film club, or both. The book club has 210 members, and the film club has 180. Hmm, let's start by recalling some set theory basics.
Since people can be in ... | [
{
"from": "human",
"value": "In a community with 350 members, each person is part of either a book club, a film club, or both. Given that 210 members are in the book club and 180 members are in the film club, how many members are exclusively in the film club?"
},
{
"from": "gpt",
"value": "<thin... |
If Mark utilizes 4 pounds of pasta to create 12 servings of fettuccine, how many pounds of pasta will he require to prepare 36 servings for a family gathering? | Since Mark utilizes 4 pounds of pasta to create 12 servings of fettuccine, we first determine how many servings can be prepared per pound of pasta:
\[
\text{Servings per pound} = \frac{12\text{ servings}}{4\text{ pounds}} = 3 \text{ servings per pound}
\]
Now, we need to calculate how many pounds of pasta are needed ... | Okay, let's see. Mark uses 4 pounds of pasta to make 12 servings. He needs to make 36 servings for a family gathering. Hmm, so I need to figure out how many pounds of pasta that would be.
First, maybe I should find out how much pasta is needed per serving. If 12 servings require 4 pounds, then each serving must take 4... | Mark uses 4 pounds of pasta to create 12 servings. To determine how many pounds of pasta he needs for 36 servings, we can use a proportion or scaling factor.
First, we recognize that 36 servings is three times the number of 12 servings. Therefore, the amount of pasta needed will also be three times the original amount... | 253 | MetaMath-AIME | <think>
Okay, let's see. Mark uses 4 pounds of pasta to make 12 servings. He needs to make 36 servings for a family gathering. Hmm, so I need to figure out how many pounds of pasta that would be.
First, maybe I should find out how much pasta is needed per serving. If 12 servings require 4 pounds, then each serving mus... | [
{
"from": "human",
"value": "If Mark utilizes 4 pounds of pasta to create 12 servings of fettuccine, how many pounds of pasta will he require to prepare 36 servings for a family gathering?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. Mark uses 4 pounds of pasta to make 12 servings. H... |
In a corporate survey, $X$ employees answered questions regarding two new policies. The survey results indicated that $340$ favored policy X and $290$ favored policy Y. If $90$ employees disapproved of both policies, how many supported both policies? If we know the answer to the above question is 120, what is the value... | To solve for the value of \( X \) in this problem, we need to analyze the provided information about the employees' survey responses regarding two policies:
1. **Total number of employees** who participated in the survey is denoted as \( X \).
2. **Favored policy X**: \( 340 \) employees.
3. **Favored policy Y**: \( 2... | Okay, let's see. I need to figure out the value of X, which is the total number of employees surveyed. The problem states that 340 employees favored policy X, 290 favored policy Y, and 90 disapproved of both policies. The answer given is that 120 employees supported both policies. So, using this information, I need to ... | To determine the value of \( X \), we use the principle of inclusion-exclusion for sets. Given that 340 employees favored policy X, 290 favored policy Y, 90 disapproved of both policies, and 120 supported both policies, we can calculate the total number of employees surveyed as follows:
1. Calculate the number of empl... | 782 | MetaMath-AIME | <think>
Okay, let's see. I need to figure out the value of X, which is the total number of employees surveyed. The problem states that 340 employees favored policy X, 290 favored policy Y, and 90 disapproved of both policies. The answer given is that 120 employees supported both policies. So, using this information, I ... | [
{
"from": "human",
"value": "In a corporate survey, $X$ employees answered questions regarding two new policies. The survey results indicated that $340$ favored policy X and $290$ favored policy Y. If $90$ employees disapproved of both policies, how many supported both policies? If we know the answer to the... |
The average score of 4 students in a math test is 82. The new average score of the remaining 3 students after one student with a score of X drops out is 84. What is the value of the unknown variable X? | To solve this problem, we need to determine the value of X, which represents the score of the student who drops out.
First, let's find the total score of the 4 students based on the average score:
1. The average score of 4 students is 82. Therefore, the total score for the 4 students is:
\[
\text{Total score} ... | Okay, let's see. The problem says that the average score of 4 students in a math test is 82. Then, after one student with a score of X drops out, the new average score of the remaining 3 students is 84. We need to find X. Hmm, averages... right, average is total divided by the number of elements. So maybe I can work wi... | The average score of 4 students in a math test is 82. Therefore, the total sum of their scores is:
\[
4 \times 82 = 328
\]
After one student with a score of \( X \) drops out, the average score of the remaining 3 students is 84. The total sum of their scores is:
\[
3 \times 84 = 252
\]
The score of the student who dr... | 541 | MetaMath-AIME | <think>
Okay, let's see. The problem says that the average score of 4 students in a math test is 82. Then, after one student with a score of X drops out, the new average score of the remaining 3 students is 84. We need to find X. Hmm, averages... right, average is total divided by the number of elements. So maybe I can... | [
{
"from": "human",
"value": "The average score of 4 students in a math test is 82. The new average score of the remaining 3 students after one student with a score of X drops out is 84. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. The prob... |
Calculate the expression X + 7^{1+1}. If we know the answer to the above question is 130, what is the value of unknown variable X? | To solve for the unknown variable X, we can set up the equation based on the information given in the question. We are told that the expression \(X + 7^{1+1}\) equals 130.
Let's simplify the expression:
\(7^{1+1} = 7^2 = 49\).
Now we can substitute this value into the equation:
\(X + 49 = 130\).
Next, to isol... | Okay, let's see. I need to find the value of X in the expression X + 7^{1+1} when the answer is 130. Hmm, alright, let's break this down step by step. First, I should probably remember the order of operations, right? PEMDAS or something like that. Parentheses, Exponents, Multiplication and Division, Addition and Subtra... | To find the value of \( X \) in the expression \( X + 7^{1+1} \) given that the answer is 130, we start by simplifying the exponent part of the expression.
First, we calculate the exponent:
\[
1 + 1 = 2
\]
Then, we compute \( 7^2 \):
\[
7^2 = 49
\]
Substituting this back into the original expression, we get:
\[
X + ... | 158 | MetaMath-AIME | <think>
Okay, let's see. I need to find the value of X in the expression X + 7^{1+1} when the answer is 130. Hmm, alright, let's break this down step by step. First, I should probably remember the order of operations, right? PEMDAS or something like that. Parentheses, Exponents, Multiplication and Division, Addition an... | [
{
"from": "human",
"value": "Calculate the expression X + 7^{1+1}. If we know the answer to the above question is 130, what is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. I need to find the value of X in the expression X + 7^{1+1} when the answer is ... |
The duration of a school assembly was 4 hours and 12 minutes. What is the total length of time in minutes? | To find the total duration of the school assembly in minutes, we can break it down as follows:
1. First, convert the hours into minutes. We know that 1 hour is equal to 60 minutes. Since there are 4 hours, we can calculate:
\[ 4 \text{ hours} = 4 \times 60 \text{ minutes} = 240 \text{ minutes} \]
2. Next, we h... | Okay, let's see. The problem says that the duration of a school assembly was 4 hours and 12 minutes, and we need to find the total length of time in minutes. Hmm, so they want the conversion of hours and minutes into just minutes. Alright, let's start breaking this down.
First, I know that 1 hour is equal to 60 minute... | To convert the duration of the school assembly from hours and minutes to just minutes, we start by converting the hours into minutes.
1 hour is equal to 60 minutes, so 4 hours is:
\[
4 \times 60 = 240 \text{ minutes}
\]
Next, we add the additional 12 minutes to the converted hours:
\[
240 + 12 = 252 \text{ minutes}
... | 686 | MetaMath-AIME | <think>
Okay, let's see. The problem says that the duration of a school assembly was 4 hours and 12 minutes, and we need to find the total length of time in minutes. Hmm, so they want the conversion of hours and minutes into just minutes. Alright, let's start breaking this down.
First, I know that 1 hour is equal to 6... | [
{
"from": "human",
"value": "The duration of a school assembly was 4 hours and 12 minutes. What is the total length of time in minutes?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. The problem says that the duration of a school assembly was 4 hours and 12 minutes, and we need to find... |
A car traveled the longest distance of 400 miles in a month and the shortest distance of X miles in another month. The longest distance is greater than the shortest distance by 100 percent. What is the value of the unknown variable X? | To solve this problem, we need to determine the value of X, which represents the shortest distance traveled by the car in another month. According to the information given, the longest distance (400 miles) is greater than the shortest distance by 100%.
When we say that one quantity is greater than another quantity by... | Okay, so I need to find the value of X, which is the shortest distance the car traveled in another month. The problem says that the longest distance, which is 400 miles, is greater than the shortest distance by 100 percent. Hmm, let me parse that.
First, the longest distance is 400 miles. The shortest distance is X mi... | The longest distance traveled by the car is 400 miles, and this distance is 100% greater than the shortest distance \( X \). To find \( X \):
1. Recognize that 100% greater than \( X \) means the longest distance is twice the shortest distance.
2. Set up the equation:
\[
2X = 400
\]
3. Solve for \( X \):
... | 1,164 | MetaMath-AIME | <think>
Okay, so I need to find the value of X, which is the shortest distance the car traveled in another month. The problem says that the longest distance, which is 400 miles, is greater than the shortest distance by 100 percent. Hmm, let me parse that.
First, the longest distance is 400 miles. The shortest distance... | [
{
"from": "human",
"value": "A car traveled the longest distance of 400 miles in a month and the shortest distance of X miles in another month. The longest distance is greater than the shortest distance by 100 percent. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<... |
Mia had X dollars at the market. She spent 5 dollars on fruit and three times that amount on vegetables. How much money does she have left? If we know the answer to the above question is 25, what is the value of unknown variable X? | To find the value of X, we need to determine how much money Mia has left after her purchases.
Initially, Mia had X dollars.
First, we note the amounts spent:
- She spent $5 on fruit.
- Then she spent three times that amount on vegetables: 3 * 5 = $15.
Now we can calculate her total spending:
Total spent = Amount on ... | Okay, let's see. The problem is about Mia who went to the market with X dollars. She spent some money on fruit and vegetables, and then had 25 dollars left. We need to find out how much she originally had, which is X.
First, let me parse the problem step by step. The question says she spent 5 dollars on fruit. Then, ... | Mia had \( X \) dollars at the market. She spent 5 dollars on fruit and three times that amount (which is \( 3 \times 5 = 15 \) dollars) on vegetables. The total amount she spent is \( 5 + 15 = 20 \) dollars. The money she has left is given by \( X - 20 \). We know this amount is 25 dollars. Therefore, we set up the eq... | 1,185 | MetaMath-AIME | <think>
Okay, let's see. The problem is about Mia who went to the market with X dollars. She spent some money on fruit and vegetables, and then had 25 dollars left. We need to find out how much she originally had, which is X.
First, let me parse the problem step by step. The question says she spent 5 dollars on fruit... | [
{
"from": "human",
"value": "Mia had X dollars at the market. She spent 5 dollars on fruit and three times that amount on vegetables. How much money does she have left? If we know the answer to the above question is 25, what is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "<thi... |
Given that a triangle has a base measuring 36 inches and a trapezoid sharing the same height and area, what is the length of the median of the trapezoid? | To find the length of the median of a trapezoid that shares the same height and area as a given triangle, we will follow these steps:
1. **Calculate the Area of the Triangle:
** \[ \text{Area}_{triangle} = \frac{1}{2} \times \text{base} \times \text{height} \]
Since we know the base is 36 inches, we need to denote ... | Okay, so I need to find the length of the median of a trapezoid that has the same area and height as a triangle with a base of 36 inches. Let me start by recalling some formulas.
First, the area of a triangle is given by (base × height)/2. The problem says the trapezoid has the same area and the same height as the tr... | Given that a triangle has a base measuring 36 inches and a trapezoid sharing the same height and area, we need to find the length of the median of the trapezoid.
First, recall the area formulas for a triangle and a trapezoid:
- The area of a triangle is \(\frac{1}{2} \times \text{base} \times \text{height}\).
- The ar... | 991 | MetaMath-AIME | <think>
Okay, so I need to find the length of the median of a trapezoid that has the same area and height as a triangle with a base of 36 inches. Let me start by recalling some formulas.
First, the area of a triangle is given by (base × height)/2. The problem says the trapezoid has the same area and the same height a... | [
{
"from": "human",
"value": "Given that a triangle has a base measuring 36 inches and a trapezoid sharing the same height and area, what is the length of the median of the trapezoid?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the length of the median of a trapezoid that has ... |
A bus travels \frac{h}{9} kilometers every r minutes. How many kilometers does the bus travel in X hours? If we know the answer to the above question is \frac{100h}{3r}, what is the value of unknown variable X? | To determine the value of X, we first need to find out how far the bus travels in X hours given its travel rate and time.
1. **Understanding the travel rate:** The bus travels \( \frac{h}{9} \) kilometers every r minutes.
2. **Finding the hourly rate:** To convert this into kilometers per hour, we need to find out ho... | Okay, so there's this problem about a bus traveling a certain distance every few minutes, and we need to figure out how many kilometers it goes in X hours. Then, apparently, the answer is given as (100h)/(3r), and we need to find X. Hmm, let me start by breaking down the problem step by step.
First, the bus travels h/... | The bus travels \(\frac{h}{9}\) kilometers every \(r\) minutes. To find the distance traveled in \(X\) hours, we first convert \(X\) hours to minutes, which is \(60X\) minutes.
The distance traveled per minute is \(\frac{h}{9r}\) kilometers. Therefore, the distance traveled in \(60X\) minutes is:
\[
\left(\frac{h}{9r... | 714 | MetaMath-AIME | <think>
Okay, so there's this problem about a bus traveling a certain distance every few minutes, and we need to figure out how many kilometers it goes in X hours. Then, apparently, the answer is given as (100h)/(3r), and we need to find X. Hmm, let me start by breaking down the problem step by step.
First, the bus tr... | [
{
"from": "human",
"value": "A bus travels \\frac{h}{9} kilometers every r minutes. How many kilometers does the bus travel in X hours? If we know the answer to the above question is \\frac{100h}{3r}, what is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so there... |
Laura bought X bananas at a cost of $30 cents per banana. She paid with a $20 bill. How much change did Laura receive? If we know the answer to the above question is 18.50, what is the value of unknown variable X? | To find the value of X, let's break down the information provided step by step.
1. **Cost of each banana**: 30 cents per banana means the cost in dollars is $0.30.
2. **Total cost for X bananas**: If she bought X bananas, the total cost is X * 0.30.
3. **Amount paid**: Laura paid with a $20 bill.
4. **Change received*... | Okay, let's tackle this problem step by step. So, Laura bought X bananas at 30 cents each and paid with a $20 bill. She received $18.50 in change. We need to find out how many bananas she bought, which is the value of X.
First, let me make sure I understand the problem correctly. The cost per banana is 30 cents, so ea... | Laura bought \( X \) bananas at a cost of $0.30 per banana. She paid with a $20 bill and received $18.50 in change. To find the value of \( X \):
1. Calculate the total cost of the bananas:
\[
\text{Total cost} = 20 - 18.50 = 1.50 \text{ dollars}
\]
2. Convert the total cost to cents to avoid decimal confusi... | 627 | MetaMath-AIME | <think>
Okay, let's tackle this problem step by step. So, Laura bought X bananas at 30 cents each and paid with a $20 bill. She received $18.50 in change. We need to find out how many bananas she bought, which is the value of X.
First, let me make sure I understand the problem correctly. The cost per banana is 30 cent... | [
{
"from": "human",
"value": "Laura bought X bananas at a cost of $30 cents per banana. She paid with a $20 bill. How much change did Laura receive? If we know the answer to the above question is 18.50, what is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's t... |
Jake's motorcycle can travel X miles on a gallon of gas, and gas costs $3 per gallon. Jake can travel 400 miles with $30 worth of gas. What is the value of the unknown variable X? | To solve this problem, we need to determine the value of X, which represents the number of miles Jake's motorcycle can travel on a gallon of gas.
Let's break down the information given:
- Cost of gas per gallon: $3
- Total amount Jake spent on gas: $30
- Total distance Jake can travel: 400 miles
First, we can find ou... | Okay, let's see here. Jake has a motorcycle that gets X miles per gallon. Gas costs $3 per gallon, and he can travel 400 miles with $30 worth of gas. I need to find X. Hmm, let me break this down step by step.
First, if gas is $3 per gallon, then $30 would buy how many gallons? Let me calculate that. Since each gallo... | Jake's motorcycle can travel \( X \) miles per gallon, and gas costs $3 per gallon. With $30 worth of gas, Jake can travel 400 miles.
First, we calculate the number of gallons Jake can buy with $30:
\[
\frac{30 \text{ dollars}}{3 \text{ dollars per gallon}} = 10 \text{ gallons}
\]
Next, we use the number of gallons ... | 1,016 | MetaMath-AIME | <think>
Okay, let's see here. Jake has a motorcycle that gets X miles per gallon. Gas costs $3 per gallon, and he can travel 400 miles with $30 worth of gas. I need to find X. Hmm, let me break this down step by step.
First, if gas is $3 per gallon, then $30 would buy how many gallons? Let me calculate that. Since ea... | [
{
"from": "human",
"value": "Jake's motorcycle can travel X miles on a gallon of gas, and gas costs $3 per gallon. Jake can travel 400 miles with $30 worth of gas. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see here. Jake has a motorcycle tha... |
In a toy factory, there are three varieties of toys whose production runs are in an arithmetic progression. The first type has 12 units produced, and each subsequent type produces 4 additional units. How many units are produced for the third type? | 1. The first type of toy has 12 units produced.
2. Each subsequent type produces 4 additional units than the previous type.
3. The second type will therefore have: 12 + 4 = 16 units.
4. For the third type, we again add 4 units to the second type's production: 16 + 4 = 20 units.
Thus, the total number of units produced... | Okay, so I need to figure out how many units are produced for the third type of toy in the factory. The problem says that the production runs are in an arithmetic progression. The first type has 12 units produced, and each subsequent type produces 4 additional units. Hmm, let me break this down step by step.
First, le... | The production runs of the toys are in an arithmetic progression (AP) where the first term is 12 units and the common difference is 4 units. To find the number of units produced for the third type, we use the formula for the nth term of an AP:
\[
a_n = a_1 + (n - 1)d
\]
Here, \(a_1 = 12\), \(d = 4\), and \(n = 3\). P... | 604 | MetaMath-AIME | <think>
Okay, so I need to figure out how many units are produced for the third type of toy in the factory. The problem says that the production runs are in an arithmetic progression. The first type has 12 units produced, and each subsequent type produces 4 additional units. Hmm, let me break this down step by step.
F... | [
{
"from": "human",
"value": "In a toy factory, there are three varieties of toys whose production runs are in an arithmetic progression. The first type has 12 units produced, and each subsequent type produces 4 additional units. How many units are produced for the third type?"
},
{
"from": "gpt",
... |
A lecture was conducted for 3 hours and X minutes. How many minutes did it last? If we know the answer to the above question is 200, what is the value of unknown variable X? | To find the total duration of the lecture in minutes, we need to convert the hours into minutes and then add the additional minutes represented by X.
1. We know that there are 60 minutes in 1 hour.
2. The lecture lasted for 3 hours, so we can convert this to minutes:
- 3 hours is equal to 3 × 60 = 180 minutes.
3. T... | Okay, let's tackle this problem. So, the question is about a lecture that lasted 3 hours and X minutes. We need to find out the value of X such that the total duration in minutes is 200. Hmm, right. Let me think through this step by step.
First, I know that 1 hour is equal to 60 minutes. So, if the lecture is 3 hours ... | The lecture lasted 3 hours and X minutes. To convert hours to minutes, we multiply by 60:
3 hours = 3 × 60 = 180 minutes.
The total duration in minutes is given as 200. Thus:
180 minutes + X minutes = 200 minutes.
Solving for \( X \):
\( X = 200 - 180 = 20 \).
**Answer:** The value of \( X \) is \(\boxed... | 678 | MetaMath-AIME | <think>
Okay, let's tackle this problem. So, the question is about a lecture that lasted 3 hours and X minutes. We need to find out the value of X such that the total duration in minutes is 200. Hmm, right. Let me think through this step by step.
First, I know that 1 hour is equal to 60 minutes. So, if the lecture is ... | [
{
"from": "human",
"value": "A lecture was conducted for 3 hours and X minutes. How many minutes did it last? If we know the answer to the above question is 200, what is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's tackle this problem. So, the question is ... |
A workshop started at 11:00 a.m. and ran for X minutes. The workshop finished at 9:00 p.m.. What is the value of the unknown variable X? | To solve this problem, we need to determine the duration of the workshop in minutes, which represents the value of X.
1. First, we determine the start time and end time of the workshop:
- Start time: 11:00 a.m.
- End time: 9:00 p.m.
2. Next, we convert both times into a 24-hour format to make calculations easie... | Okay, so I need to figure out how many minutes the workshop lasted. It started at 11:00 a.m. and ended at 9:00 p.m. Hmm, let me think. First, I should figure out the total time between 11:00 a.m. and 9:00 p.m. in hours, and then convert that to minutes since the answer needs to be in X minutes.
Let me start by counti... | The workshop started at 11:00 a.m. and ended at 9:00 p.m. To find the duration \( X \):
1. Calculate the total hours:
From 11:00 a.m. to 12:00 p.m. = 1 hour.
From 12:00 p.m. to 9:00 p.m. = 9 hours.
Total hours = \( 1 + 9 = 10 \) hours.
2. Convert hours to minutes:
\( 10 \text{ hours} \times 60 \te... | 270 | MetaMath-AIME | <think>
Okay, so I need to figure out how many minutes the workshop lasted. It started at 11:00 a.m. and ended at 9:00 p.m. Hmm, let me think. First, I should figure out the total time between 11:00 a.m. and 9:00 p.m. in hours, and then convert that to minutes since the answer needs to be in X minutes.
Let me start b... | [
{
"from": "human",
"value": "A workshop started at 11:00 a.m. and ran for X minutes. The workshop finished at 9:00 p.m.. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out how many minutes the workshop lasted. It started at 11:00 a.... |
What is the value of \[3 - (-4) + 5 - (-6) - X + 1?\] If we know the answer to the above question is 17, what is the value of unknown variable X? | To solve the equation, we can start by simplifying the left side step by step:
1. Start with the expression: 3 - (-4) + 5 - (-6) - X + 1
2. Rewrite the expression by converting the subtraction of a negative into an addition:
- 3 + 4 + 5 + 6 - X + 1
3. Now, we can add the constants together:
- (3 + 4 + 5 + 6 + ... | Okay, so I need to find the value of X in the equation 3 - (-4) + 5 - (-6) - X + 1 = 17. Hmm, let me start by simplifying the left side step by step.
First, let me remember that subtracting a negative is the same as adding a positive. So, whenever I see something like - (-number), that becomes + number. Let me apply ... | To find the value of \( X \) in the equation \( 3 - (-4) + 5 - (-6) - X + 1 = 17 \), we start by simplifying the left side step by step.
First, we handle the subtraction of negatives:
\[
3 - (-4) = 3 + 4 = 7
\]
\[
5 - (-6) = 5 + 6 = 11
\]
Substituting these back into the equation, we get:
\[
7 + 11 - X + 1
\]
Next, ... | 545 | MetaMath-AIME | <think>
Okay, so I need to find the value of X in the equation 3 - (-4) + 5 - (-6) - X + 1 = 17. Hmm, let me start by simplifying the left side step by step.
First, let me remember that subtracting a negative is the same as adding a positive. So, whenever I see something like - (-number), that becomes + number. Let m... | [
{
"from": "human",
"value": "What is the value of \\[3 - (-4) + 5 - (-6) - X + 1?\\] If we know the answer to the above question is 17, what is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the value of X in the equation 3 - (-4) + 5 - (-6) - X ... |
Ms. Johnson measures her square patio, determining that each side measures 12 steps. Given that each step is 3 feet long, how many pounds of tomatoes can she anticipate harvesting if she expects to gather 0.75 pounds of tomatoes for every square foot? | The area of Ms. Johnson's square patio can be calculated using the formula for the area of a square:
\[ \text{Area} = \text{side}^2 \]
Since each side measures 12 steps, we first need to convert this measurement into feet:
\[ \text{side in feet} = 12 \text{ steps} \times 3 \text{ feet/step} = 36 \text{ feet} \]
Now w... | Okay, so Ms. Johnson has this square patio, right? And she measured each side, and each side is 12 steps long. Each step is 3 feet. Hmm, so first, I think I need to figure out the area of the patio in square feet because the tomatoes are harvested per square foot. Let me start by converting the steps into feet.
If eac... | Ms. Johnson's square patio has sides measuring 12 steps, with each step equal to 3 feet. Converting the side length to feet:
\[
12 \text{ steps} \times 3 \text{ feet/step} = 36 \text{ feet}
\]
The area of the patio is:
\[
36 \text{ feet} \times 36 \text{ feet} = 1,296 \text{ square feet}
\]
Given a yield of 0.7... | 528 | MetaMath-AIME | <think>
Okay, so Ms. Johnson has this square patio, right? And she measured each side, and each side is 12 steps long. Each step is 3 feet. Hmm, so first, I think I need to figure out the area of the patio in square feet because the tomatoes are harvested per square foot. Let me start by converting the steps into feet.... | [
{
"from": "human",
"value": "Ms. Johnson measures her square patio, determining that each side measures 12 steps. Given that each step is 3 feet long, how many pounds of tomatoes can she anticipate harvesting if she expects to gather 0.75 pounds of tomatoes for every square foot?"
},
{
"from": "gpt"... |
Luke and Jane each have cylindrical containers for their paint. Luke's container has a diameter of 8 cm and a height of X cm. Jane's container has a diameter of 16 cm and a height of 4 cm. What is the ratio of the volume of Luke's container to the volume of Jane's container? If we know the answer to the above question ... | To solve this problem, we need to calculate the volumes of both cylindrical containers and set up a ratio based on the given information. The volume \( V \) of a cylinder is calculated using the formula:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cylinder.
**Step 1: Calculate th... | Okay, let's see. So, the problem is about Luke and Jane's cylindrical paint containers. We need to find the ratio of their volumes and then determine the height (X) of Luke's container if the ratio is 1:1.
First, I remember that the volume of a cylinder is calculated using the formula V = πr²h, where r is the radius a... | To find the value of the unknown variable \( X \), we start by calculating the volumes of Luke's and Jane's cylindrical containers using the formula for the volume of a cylinder, \( V = \pi r^2 h \).
For Luke's container:
- Diameter = 8 cm, so radius \( r = \frac{8}{2} = 4 \) cm.
- Height = \( X \) cm.
- Volume \( V_1... | 823 | MetaMath-AIME | <think>
Okay, let's see. So, the problem is about Luke and Jane's cylindrical paint containers. We need to find the ratio of their volumes and then determine the height (X) of Luke's container if the ratio is 1:1.
First, I remember that the volume of a cylinder is calculated using the formula V = πr²h, where r is the ... | [
{
"from": "human",
"value": "Luke and Jane each have cylindrical containers for their paint. Luke's container has a diameter of 8 cm and a height of X cm. Jane's container has a diameter of 16 cm and a height of 4 cm. What is the ratio of the volume of Luke's container to the volume of Jane's container? If ... |
A list contains six numbers, where the average of the first three is 4 and the average of the last three is 9. Given that the average of all six numbers is 6, what is the value of the number that appears in both groups? | Let the six numbers be represented as \(a, b, c, d, e, f\). According to the problem, we can set up the following equations based on the averages provided:
1. The average of the first three numbers \(a, b, c\) is 4:
\[\frac{a + b + c}{3} = 4 \implies a + b + c = 12.\]
2. The average of the last three numbers ... | Okay, let's see. I have this problem where there's a list of six numbers. The average of the first three is 4, the average of the last three is 9, and the overall average of all six numbers is 6. I need to find the value of the number that's in both groups. Hmm, so there's a number that's counted in both the first thre... | Given a list of six numbers where the average of the first three is 4, the average of the last three is 9, and the average of all six numbers is 6, we need to find the value of the number that appears in both groups.
1. The sum of the first three numbers is \(3 \times 4 = 12\).
2. The sum of the last three numbers is ... | 1,030 | MetaMath-AIME | <think>
Okay, let's see. I have this problem where there's a list of six numbers. The average of the first three is 4, the average of the last three is 9, and the overall average of all six numbers is 6. I need to find the value of the number that's in both groups. Hmm, so there's a number that's counted in both the fi... | [
{
"from": "human",
"value": "A list contains six numbers, where the average of the first three is 4 and the average of the last three is 9. Given that the average of all six numbers is 6, what is the value of the number that appears in both groups?"
},
{
"from": "gpt",
"value": "<think>\nOkay, l... |
If a fuel tank displays 75 liters when it is 25% full, what is the total capacity of the fuel tank when it is completely filled? | 1. Determine the amount of fuel in the tank when it is 25% full.
- The tank shows 75 liters, and this represents 25% of the total capacity.
2. Let the total capacity of the tank be represented as \( C \).
- Since 75 liters is 25% of \( C \), we can write the equation: \( 0.25C = 75 \).
3. To find the total c... | Okay, so the problem here is that a fuel tank shows 75 liters when it's 25% full, and we need to figure out the total capacity when it's completely full. Hmm, let me think. Alright, percentages can sometimes be tricky, but let's break it down step by step.
First, let's understand what 25% full means. If the tank is 25... | If a fuel tank displays 75 liters when it is 25% full, we need to determine the total capacity of the tank when it is completely filled.
Given that 25% of the tank's capacity is 75 liters, we can represent the total capacity as \( C \). Mathematically, this is expressed as:
\[
0.25 \times C = 75
\]
To find \( C \), ... | 1,236 | MetaMath-AIME | <think>
Okay, so the problem here is that a fuel tank shows 75 liters when it's 25% full, and we need to figure out the total capacity when it's completely full. Hmm, let me think. Alright, percentages can sometimes be tricky, but let's break it down step by step.
First, let's understand what 25% full means. If the ta... | [
{
"from": "human",
"value": "If a fuel tank displays 75 liters when it is 25% full, what is the total capacity of the fuel tank when it is completely filled?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so the problem here is that a fuel tank shows 75 liters when it's 25% full, and we need to f... |
James runs in a park. Initially, he completed X laps in 45 minutes. Now, he can finish 18 laps in 36 minutes. He has improved his lap time by 1 minute. What is the value of the unknown variable X? | To solve this problem, we need to determine the value of X, which represents the number of laps James initially completed in 45 minutes. \n\n1. First, let's calculate James's current lap time after improvement. He can finish 18 laps in 36 minutes. \n - Current lap time = Total time / Number of laps = 36 minutes / 18 ... | Okay, let's see. James used to run X laps in 45 minutes. Now he can do 18 laps in 36 minutes, and his lap time has improved by 1 minute per lap. I need to find X. Hmm.
First, let me figure out what "improved his lap time by 1 minute" means. So, his time per lap now is 1 minute less than before. That means if before h... | James initially completed \( X \) laps in 45 minutes, so his initial lap time was \( \frac{45}{X} \) minutes per lap. Now, he can finish 18 laps in 36 minutes, which means his current lap time is \( \frac{36}{18} = 2 \) minutes per lap.
Since his lap time has improved by 1 minute, his initial lap time must be 1 minut... | 1,129 | MetaMath-AIME | <think>
Okay, let's see. James used to run X laps in 45 minutes. Now he can do 18 laps in 36 minutes, and his lap time has improved by 1 minute per lap. I need to find X. Hmm.
First, let me figure out what "improved his lap time by 1 minute" means. So, his time per lap now is 1 minute less than before. That means if ... | [
{
"from": "human",
"value": "James runs in a park. Initially, he completed X laps in 45 minutes. Now, he can finish 18 laps in 36 minutes. He has improved his lap time by 1 minute. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. James used to... |
Mr. Adams measures his rectangular orchard and finds it is X steps by 30 steps. Each of Mr. Adams's steps is 2 feet long. He anticipates 0.3 pounds of apples per square foot from his orchard. Mr. Adams's expected yield of apples is 900. What is the value of the unknown variable X? | To solve this problem, we first need to understand the relationship between the dimensions of Mr. Adams's orchard, the area of the orchard, and the expected yield of apples.
1. **Dimensions of the Orchard:**
Mr. Adams’s orchard is rectangular with dimensions X steps by 30 steps.
2. **Area Calculation:**
... | Okay, let's try to figure out the value of X here. So, Mr. Adams has a rectangular orchard that's X steps by 30 steps. Each step he takes is 2 feet long. Hmm, so first, I need to convert those steps into actual feet to find the area of the orchard in square feet, right?
Alright, if each step is 2 feet, then the length... | Mr. Adams's rectangular orchard is \( X \) steps by 30 steps, with each step being 2 feet long. To find the area of the orchard in square feet, we convert the steps to feet:
\[
\text{Length} = X \text{ steps} \times 2 \text{ feet/step} = 2X \text{ feet}
\]
\[
\text{Width} = 30 \text{ steps} \times 2 \text{ feet/step} ... | 330 | MetaMath-AIME | <think>
Okay, let's try to figure out the value of X here. So, Mr. Adams has a rectangular orchard that's X steps by 30 steps. Each step he takes is 2 feet long. Hmm, so first, I need to convert those steps into actual feet to find the area of the orchard in square feet, right?
Alright, if each step is 2 feet, then th... | [
{
"from": "human",
"value": "Mr. Adams measures his rectangular orchard and finds it is X steps by 30 steps. Each of Mr. Adams's steps is 2 feet long. He anticipates 0.3 pounds of apples per square foot from his orchard. Mr. Adams's expected yield of apples is 900. What is the value of the unknown variable ... |
A survey of 750 people asked about their vacation preferences. X preferred beach vacations, 250 preferred mountain vacations, and the rest preferred city vacations. The ratio of those who preferred beach vacations to those who preferred mountain vacations is 6/5. What is the value of the unknown variable X? | To solve the problem, we need to set up an equation based on the information given about vacation preferences.
1. **Total people surveyed**: 750
2. **People who preferred mountain vacations**: 250 (given)
3. **People who preferred beach vacations**: X (unknown)
4. **People who preferred city vacations**: 750 - X -... | Okay, let's see. There's this survey of 750 people, and they were asked about their vacation preferences. The problem says that X preferred beach vacations, 250 preferred mountain vacations, and the rest preferred city vacations. Also, the ratio of beach to mountain vacations is 6/5. We need to find X, which is the num... | Given a survey of 750 people where 250 preferred mountain vacations and the rest preferred either beach or city vacations, we need to find the number of people who preferred beach vacations, denoted as \( X \). The ratio of those who preferred beach vacations to those who preferred mountain vacations is given as \( \fr... | 61 | MetaMath-AIME | <think>
Okay, let's see. There's this survey of 750 people, and they were asked about their vacation preferences. The problem says that X preferred beach vacations, 250 preferred mountain vacations, and the rest preferred city vacations. Also, the ratio of beach to mountain vacations is 6/5. We need to find X, which is... | [
{
"from": "human",
"value": "A survey of 750 people asked about their vacation preferences. X preferred beach vacations, 250 preferred mountain vacations, and the rest preferred city vacations. The ratio of those who preferred beach vacations to those who preferred mountain vacations is 6/5. What is the val... |
Mia has 5 walls in her workshop that require painting. Each wall measures 15 feet in height and 10 feet in width. Since cellar windows and doors that do not need painting occupy a total of 90 square feet, what is the total wall area that requires paint? | 1. First, calculate the area of one wall. The formula for the area of a rectangle is width multiplied by height:
\[ \text{Area of one wall} = \text{height} \times \text{width} = 15 \text{ ft} \times 10 \text{ ft} = 150 \text{ square feet} \]
2. Now, since there are 5 walls, we can find the total area of all 5 walls... | Okay, let me try to figure out how to solve this problem. So, Mia has 5 walls in her workshop that need painting. Each wall is 15 feet high and 10 feet wide. But there are some cellar windows and doors that don't need painting, and their total area is 90 square feet. The question is asking for the total wall area that ... | Mia has 5 walls in her workshop that require painting. Each wall measures 15 feet in height and 10 feet in width. The total area of the walls before subtracting the non-paintable areas is calculated as follows:
\[
\text{Area of one wall} = 15 \, \text{feet} \times 10 \, \text{feet} = 150 \, \text{square feet}
\]
\[
\... | 1,066 | MetaMath-AIME | <think>
Okay, let me try to figure out how to solve this problem. So, Mia has 5 walls in her workshop that need painting. Each wall is 15 feet high and 10 feet wide. But there are some cellar windows and doors that don't need painting, and their total area is 90 square feet. The question is asking for the total wall ar... | [
{
"from": "human",
"value": "Mia has 5 walls in her workshop that require painting. Each wall measures 15 feet in height and 10 feet in width. Since cellar windows and doors that do not need painting occupy a total of 90 square feet, what is the total wall area that requires paint?"
},
{
"from": "gp... |
Michael had a collection of 300 marbles. He sold 40% of them to David. Next, he sold 15% of the remaining marbles to Sarah. After that, he gave away X marbles to his little brother. Michael has 148 marbles left. What is the value of the unknown variable X? | To solve this problem, we should break it down into steps based on the transactions that Michael made with his marbles:
1. **Calculating the initial number of marbles sold to David**:
- Michael started with 300 marbles.
- He sold 40% of them to David:
\[ 0.40 \times 300 = 120 \text{ marbles} \]
- So, af... | Okay, let's see. Michael had 300 marbles initially. He sold 40% of them to David first. Then he sold 15% of the remaining marbles to Sarah. After that, he gave away X marbles to his little brother and ended up with 148 marbles. I need to find X.
Alright, step by step. First, let's figure out how many marbles he sold t... | Michael initially had 300 marbles. He sold 40% of them to David:
\[
40\% \text{ of } 300 = 0.4 \times 300 = 120
\]
Remaining marbles after selling to David:
\[
300 - 120 = 180
\]
Next, he sold 15% of the remaining 180 marbles to Sarah:
\[
15\% \text{ of } 180 = 0.15 \times 180 = 27
\]
Remaining marbles after sell... | 162 | MetaMath-AIME | <think>
Okay, let's see. Michael had 300 marbles initially. He sold 40% of them to David first. Then he sold 15% of the remaining marbles to Sarah. After that, he gave away X marbles to his little brother and ended up with 148 marbles. I need to find X.
Alright, step by step. First, let's figure out how many marbles h... | [
{
"from": "human",
"value": "Michael had a collection of 300 marbles. He sold 40% of them to David. Next, he sold 15% of the remaining marbles to Sarah. After that, he gave away X marbles to his little brother. Michael has 148 marbles left. What is the value of the unknown variable X?"
},
{
"from": ... |
In Maplewood, 18 fitness centers have an average of 2,250 gym memberships each. What is the overall total number of gym memberships for all the centers combined? | To find the overall total number of gym memberships for all the fitness centers in Maplewood, we need to multiply the average number of memberships per center by the total number of fitness centers. Thus:
1. The average number of gym memberships per fitness center = 2,250.
2. The number of fitness centers = 18.
Now w... | Okay, so I need to find the total number of gym memberships across all 18 fitness centers in Maplewood. The problem says that each center has an average of 2,250 memberships. Hmm, averages can sometimes be tricky, but I think I remember that the average is calculated by taking the total and dividing by the number of it... | To find the overall total number of gym memberships for all 18 fitness centers in Maplewood, we start with the given average number of memberships per center, which is 2,250. The formula for the total number of memberships is:
\[
\text{Total} = \text{Average} \times \text{Number of Items}
\]
Here, the average is 2,25... | 21 | MetaMath-AIME | <think>
Okay, so I need to find the total number of gym memberships across all 18 fitness centers in Maplewood. The problem says that each center has an average of 2,250 memberships. Hmm, averages can sometimes be tricky, but I think I remember that the average is calculated by taking the total and dividing by the numb... | [
{
"from": "human",
"value": "In Maplewood, 18 fitness centers have an average of 2,250 gym memberships each. What is the overall total number of gym memberships for all the centers combined?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the total number of gym memberships acros... |
If pizza slices at Tony's Pizzeria are priced at $4 each and garlic bread at $3 each, what will be the total cost to buy 6 pizza slices and 4 garlic breads? | First, we calculate the cost of the pizza slices:
- Each pizza slice costs $4.
- If we buy 6 slices, the total cost for the pizza is:
\[ 6 \times 4 = 24 \text{ dollars} \]
Next, we calculate the cost of the garlic bread:
- Each garlic bread costs $3.
- If we buy 4 garlic breads, the total cost for the garlic br... | Okay, so I need to figure out the total cost for buying 6 pizza slices and 4 garlic breads at Tony's Pizzeria. Let me start by breaking down the problem step by step.
First, the pizza slices are priced at $4 each. If I want to buy 6 of them, I should multiply the price per slice by the number of slices. That makes se... | The total cost for 6 pizza slices and 4 garlic breads is calculated as follows:
- **Pizza slices**: 6 slices × $4/slice = $24
- **Garlic breads**: 4 × $3 each = $12
**Total cost**: $24 + $12 = **$36**
**Answer:** The total cost is $\boxed{36}$. | 189 | MetaMath-AIME | <think>
Okay, so I need to figure out the total cost for buying 6 pizza slices and 4 garlic breads at Tony's Pizzeria. Let me start by breaking down the problem step by step.
First, the pizza slices are priced at $4 each. If I want to buy 6 of them, I should multiply the price per slice by the number of slices. That ... | [
{
"from": "human",
"value": "If pizza slices at Tony's Pizzeria are priced at $4 each and garlic bread at $3 each, what will be the total cost to buy 6 pizza slices and 4 garlic breads?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out the total cost for buying 6 pizza slices... |
Sophie swims a distance of X miles in 45 minutes. Her average speed is 2 miles per hour. What is the value of the unknown variable X? | To solve this problem, we first need to understand the relationship between distance, speed, and time. The formula to calculate distance is given by:
Distance = Speed × Time
We are told that Sophie's average speed is 2 miles per hour and she swims for 45 minutes. First, we need to convert the time from minutes to h... | Okay, let me try to figure this out. So, Sophie swims a distance of X miles in 45 minutes, and her average speed is 2 miles per hour. I need to find X. Hmm, let's see.
First, I remember that speed is equal to distance divided by time. The formula is speed = distance/time. But here, the speed is given in miles per hou... | Sophie swims a distance of \( X \) miles in 45 minutes, and her average speed is 2 miles per hour. To find \( X \), we need to use the formula for distance, which is speed multiplied by time.
First, convert the time from minutes to hours:
\[
45 \text{ minutes} = \frac{45}{60} \text{ hours} = 0.75 \text{ hours}
\]
Us... | 609 | MetaMath-AIME | <think>
Okay, let me try to figure this out. So, Sophie swims a distance of X miles in 45 minutes, and her average speed is 2 miles per hour. I need to find X. Hmm, let's see.
First, I remember that speed is equal to distance divided by time. The formula is speed = distance/time. But here, the speed is given in miles... | [
{
"from": "human",
"value": "Sophie swims a distance of X miles in 45 minutes. Her average speed is 2 miles per hour. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let me try to figure this out. So, Sophie swims a distance of X miles in 45 minutes, an... |
A parent tells their child, "Pick a number, subtract X from it, and multiply the result by 5. Give that number to your sibling. Sibling, divide the number by 2 and add 10 to find your result." Lily thinks of 10, and gives the number to Tom. Tom's result is 30. What is the value of the unknown variable X? | To solve the problem, we'll break down the steps that Lily and Tom take, and set up an equation that helps us find the unknown variable X.
1. **Lily's Calculation**:
- Lily picks a number, which is 10.
- She subtracts X from this number: 10 - X.
- Then, she multiplies the result by 5: (10 - X) * 5.
2. **Giv... | Okay, let me try to figure out this problem. So, the parent tells the child to pick a number, subtract X from it, multiply the result by 5, and give that number to the sibling. Then the sibling is supposed to divide the number by 2 and add 10 to get the result. Lily picks 10, gives the number to Tom, and Tom ends up wi... | Lily picks the number 10. She subtracts \( X \) from it, resulting in \( 10 - X \). She then multiplies the result by 5, giving the number \( 5(10 - X) \) to Tom. Tom divides this number by 2 and adds 10, resulting in 30. We need to find \( X \).
Starting with the equation based on Tom's result:
\[
\frac{5(10 - X)}{2}... | 836 | MetaMath-AIME | <think>
Okay, let me try to figure out this problem. So, the parent tells the child to pick a number, subtract X from it, multiply the result by 5, and give that number to the sibling. Then the sibling is supposed to divide the number by 2 and add 10 to get the result. Lily picks 10, gives the number to Tom, and Tom en... | [
{
"from": "human",
"value": "A parent tells their child, \"Pick a number, subtract X from it, and multiply the result by 5. Give that number to your sibling. Sibling, divide the number by 2 and add 10 to find your result.\" Lily thinks of 10, and gives the number to Tom. Tom's result is 30. What is the valu... |
Emma's hybrid car drives X miles per gallon, and gas is priced at $2.50 per gallon. How far can Emma go with $25 worth of gas? If we know the answer to the above question is 500, what is the value of unknown variable X? | To solve this problem, we need to determine the value of X, which represents the miles per gallon that Emma's hybrid car can drive.
Let's break down the information given:
- The price of gas is $2.50 per gallon.
- Emma can purchase $25 worth of gas.
First, we need to find out how many gallons of gas Emma can buy wit... | Okay, let's see. Emma has a hybrid car that gets X miles per gallon. Gas costs $2.50 per gallon. She wants to know how far she can drive with $25 worth of gas. And apparently, the answer is 500 miles. So we need to find X, which is the car's miles per gallon.
Hmm, let's start by breaking down the problem. First, Emma... | Emma can drive 500 miles with $25 worth of gas. To find the car's fuel efficiency \( X \):
1. **Gallons purchased**:
\[
\frac{\$25}{\$2.50/\text{gallon}} = 10 \text{ gallons}
\]
2. **Miles driven**:
\[
10 \text{ gallons} \times X \frac{\text{miles}}{\text{gallon}} = 500 \text{ miles}
\]
3. **So... | 474 | MetaMath-AIME | <think>
Okay, let's see. Emma has a hybrid car that gets X miles per gallon. Gas costs $2.50 per gallon. She wants to know how far she can drive with $25 worth of gas. And apparently, the answer is 500 miles. So we need to find X, which is the car's miles per gallon.
Hmm, let's start by breaking down the problem. Fir... | [
{
"from": "human",
"value": "Emma's hybrid car drives X miles per gallon, and gas is priced at $2.50 per gallon. How far can Emma go with $25 worth of gas? If we know the answer to the above question is 500, what is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, l... |
What is the value of 3 + X + 8 - (-4) - 2? If we know the answer to the above question is 8, what is the value of unknown variable X? | To solve for X in the equation provided, let's first simplify and set up the equation step by step.
We start with the expression: 3 + X + 8 - (-4) - 2.
1. First, we simplify - (-4) which becomes +4:
So the equation is now: 3 + X + 8 + 4 - 2.
2. Next, combine the constants (3 + 8 + 4 - 2):
3 + 8 = 11,
11 + 4... | Okay, let's see here. The problem is asking for the value of X in the equation 3 + X + 8 - (-4) - 2, and we know that the answer is 8. Hmm, let me break this down step by step.
First, I need to simplify the expression as much as possible without the variable X. Let me rewrite the equation to make sure I understand it ... | The given expression is \(3 + X + 8 - (-4) - 2\). Simplifying the constants step by step:
1. Combine \(3 + 8 = 11\).
2. Simplify \(-(-4)\) to \(+4\).
3. Combine the constants: \(11 + 4 - 2 = 13\).
This reduces the expression to \(13 + X\). Given that the result is 8:
\[
13 + X = 8
\]
Solving for \(X\):
\[
X = 8 - ... | 840 | MetaMath-AIME | <think>
Okay, let's see here. The problem is asking for the value of X in the equation 3 + X + 8 - (-4) - 2, and we know that the answer is 8. Hmm, let me break this down step by step.
First, I need to simplify the expression as much as possible without the variable X. Let me rewrite the equation to make sure I unders... | [
{
"from": "human",
"value": "What is the value of 3 + X + 8 - (-4) - 2? If we know the answer to the above question is 8, what is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see here. The problem is asking for the value of X in the equation 3 + X + 8 - (-... |
When the radius of a circle is increased by 30%, what is the percentage increase in the area of the circle? | Let's denote the original radius of the circle as \( r \). The area of a circle is given by the formula \( A = \pi r^2 \).
1. **Calculate the original area of the circle:**
- \( A_{original} = \pi r^2 \)
2. **Increase the radius by 30%:**
- New radius \( r_{new} = r + 0.30r = 1.30r \)
3. **Calculate ... | Okay, so I need to figure out the percentage increase in the area of a circle when its radius is increased by 30%. Hmm, let's start by recalling the formula for the area of a circle. I think it's A = πr², right? Yeah, that sounds familiar. So the area depends on the square of the radius.
Alright, if the radius is inc... | To determine the percentage increase in the area of a circle when its radius is increased by 30%, we start with the formula for the area of a circle, \( A = \pi r^2 \).
When the radius is increased by 30%, the new radius becomes \( 1.3r \). Substituting this into the area formula, we get the new area:
\[
A' = \pi (1.3... | 1,218 | MetaMath-AIME | <think>
Okay, so I need to figure out the percentage increase in the area of a circle when its radius is increased by 30%. Hmm, let's start by recalling the formula for the area of a circle. I think it's A = πr², right? Yeah, that sounds familiar. So the area depends on the square of the radius.
Alright, if the radiu... | [
{
"from": "human",
"value": "When the radius of a circle is increased by 30%, what is the percentage increase in the area of the circle?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out the percentage increase in the area of a circle when its radius is increased by 30%. Hmm,... |
Tom was instructed to divide a certain number by X and then add 6. Instead, he added 6 first and then divided the result by 2, giving an answer of 15. The correct answer would have been 12. What is the value of the unknown variable X? | To solve this problem, we need to set up equations based on the operations described and solve for the unknown variable X.
Let the certain number be represented as N.
1. **Correct operation:** Tom was supposed to divide the number, N, by X and then add 6.
- This gives us the correct answer of 12:
\[ \frac{N}{X}... | Okay, let's try to solve this problem step by step. So, the problem is about Tom who was supposed to divide a certain number by X and then add 6, but instead he added 6 first and then divided by 2, getting 15. The correct answer should have been 12. We need to find X.
First, let me make sure I understand the problem c... | Let \( N \) be the certain number. According to the problem, Tom was supposed to divide \( N \) by \( X \) and then add 6, resulting in 12. However, Tom added 6 to \( N \) first and then divided by 2, resulting in 15. We need to find \( X \).
First, solve Tom's incorrect equation to find \( N \):
\[
\frac{N + 6}{2} = ... | 480 | MetaMath-AIME | <think>
Okay, let's try to solve this problem step by step. So, the problem is about Tom who was supposed to divide a certain number by X and then add 6, but instead he added 6 first and then divided by 2, getting 15. The correct answer should have been 12. We need to find X.
First, let me make sure I understand the p... | [
{
"from": "human",
"value": "Tom was instructed to divide a certain number by X and then add 6. Instead, he added 6 first and then divided the result by 2, giving an answer of 15. The correct answer would have been 12. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<... |
In a box filled with marbles and dice, it is stated that ten percent of the items are dice. Moreover, sixty percent of the marbles are blue. What percentage of the total items in the box consists of blue marbles? | To determine the percentage of blue marbles in the box, let's denote the total number of items in the box as \( T \). \n
1. **Items Composition:** Given that 10% of the items are dice, this means that the number of dice is: \[ \text{Number of dice} = 0.1T \]
Consequently, the remaining items, which are marbles, wi... | Okay, let's see. The problem is about a box that has marbles and dice. It says that ten percent of the items are dice, which means the remaining ninety percent must be marbles, right? Because if 10% are dice, then 100% - 10% = 90% are marbles. Got that part.
Then, it mentions that sixty percent of the marbles are blue... | Given that ten percent of the items in the box are dice, the remaining ninety percent must be marbles. Sixty percent of these marbles are blue. To find the percentage of blue marbles out of the total items, we can follow these steps:
1. **Assume the total number of items is 100** for simplicity.
2. **Calculate the num... | 1,067 | MetaMath-AIME | <think>
Okay, let's see. The problem is about a box that has marbles and dice. It says that ten percent of the items are dice, which means the remaining ninety percent must be marbles, right? Because if 10% are dice, then 100% - 10% = 90% are marbles. Got that part.
Then, it mentions that sixty percent of the marbles ... | [
{
"from": "human",
"value": "In a box filled with marbles and dice, it is stated that ten percent of the items are dice. Moreover, sixty percent of the marbles are blue. What percentage of the total items in the box consists of blue marbles?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's se... |
Which cylinder has X the volume of the cylinder with radius 3 and height 10? If we know the answer to the above question is 180π, what is the value of unknown variable X? | To solve this problem, we first need to calculate the volume of a cylinder using the formula:
\[ V = \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
Given:
- Radius, \( r = 3 \)
- Height, \( h = 10 \)
Now, we can substitute these values into the formula:
\[ V = \pi (3)^2... | Okay, let's see. The problem is asking: Which cylinder has X the volume of the cylinder with radius 3 and height 10? And then we're told that the answer is 180π, and we need to find X. Hmm, so I think X is a multiplier here. Let me try to break this down step by step.
First, I remember that the volume of a cylinder is... | To determine the value of \( X \), we start by calculating the volume of the original cylinder with radius 3 and height 10 using the formula for the volume of a cylinder, \( V = \pi r^2 h \).
\[
V = \pi (3)^2 (10) = \pi \times 9 \times 10 = 90\pi
\]
We know that the volume of the other cylinder is \( 180\pi \). This ... | 324 | MetaMath-AIME | <think>
Okay, let's see. The problem is asking: Which cylinder has X the volume of the cylinder with radius 3 and height 10? And then we're told that the answer is 180π, and we need to find X. Hmm, so I think X is a multiplier here. Let me try to break this down step by step.
First, I remember that the volume of a cyl... | [
{
"from": "human",
"value": "Which cylinder has X the volume of the cylinder with radius 3 and height 10? If we know the answer to the above question is 180π, what is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. The problem is asking: Which cylinder h... |
Eight markers are placed evenly along a walking path. The distance from the first marker to the sixth is X meters. What is the distance between the first and the eighth marker? If we know the answer to the above question is 126, what is the value of unknown variable X? | To solve for the unknown variable X, we start by analyzing the markers placed along the walking path:
1. **Identify the markers**: The markers are numbered from 1 to 8. The distance from the first marker to the sixth marker is given as X meters.
2. **Determine the number of intervals**: The distance from the first ma... | Okay, let's see. There are eight markers placed evenly along a walking path. The distance from the first marker to the sixth is X meters. We need to find the distance between the first and the eighth marker, but actually, we know that the answer is 126 meters, so we have to find X. Hmm, let's break this down step by st... | Given eight markers placed evenly along a walking path, the distance from the first marker to the sixth is \( X \) meters. We need to find the value of \( X \) given that the distance from the first to the eighth marker is 126 meters.
1. The distance between consecutive markers is denoted as \( d \).
2. The distance f... | 103 | MetaMath-AIME | <think>
Okay, let's see. There are eight markers placed evenly along a walking path. The distance from the first marker to the sixth is X meters. We need to find the distance between the first and the eighth marker, but actually, we know that the answer is 126 meters, so we have to find X. Hmm, let's break this down st... | [
{
"from": "human",
"value": "Eight markers are placed evenly along a walking path. The distance from the first marker to the sixth is X meters. What is the distance between the first and the eighth marker? If we know the answer to the above question is 126, what is the value of unknown variable X?"
},
{... |
A group of players plays volleyball for 75 minutes, with six players on the court at once among a total of X players. How long can each player be on the court? If we know the answer to the above question is 37.5, what is the value of unknown variable X? | To solve this problem, we need to determine how long each player can be on the court given that there are a total of X players and 6 players playing at any one time during a 75-minute game.
Let's break down the information:
- Total playing time of the game: 75 minutes
- Number of players on the court at once: 6 player... | Okay, let's try to figure out this volleyball problem. So, there's a group of players who play volleyball for 75 minutes. At any given time, there are six players on the court. The total number of players is X, and we need to find X given that each player can be on the court for 37.5 minutes. Hmm, okay.
Let me start b... | Given that a group of players plays volleyball for 75 minutes with six players on the court at any given time, we need to determine the total number of players \( X \) if each player is on the court for 37.5 minutes.
First, calculate the total player-minutes by multiplying the total game time by the number of players ... | 1,033 | MetaMath-AIME | <think>
Okay, let's try to figure out this volleyball problem. So, there's a group of players who play volleyball for 75 minutes. At any given time, there are six players on the court. The total number of players is X, and we need to find X given that each player can be on the court for 37.5 minutes. Hmm, okay.
Let me... | [
{
"from": "human",
"value": "A group of players plays volleyball for 75 minutes, with six players on the court at once among a total of X players. How long can each player be on the court? If we know the answer to the above question is 37.5, what is the value of unknown variable X?"
},
{
"from": "gp... |
Emma checks her car's odometer which reads X miles. After a 4-hour drive today and 6 hours the next day, she sees that it now reads 5310 miles. What was her average speed in miles per hour? If we know the answer to the above question is 3, what is the value of unknown variable X? | To solve this problem, we first need to figure out how many miles Emma drove in total and then determine her average speed during that time.
Let's break down the information given:
- After a 4-hour drive today and 6 hours the next day, her car's odometer reads 5310 miles.
- The total driving time is 4 hours + 6 hours ... | Okay, so Emma checked her car's odometer and it showed X miles. Then she drove for 4 hours one day and 6 hours the next day, and after that, the odometer reads 5310 miles. The question is asking for her average speed in miles per hour, and we already know the answer is 3. So, we need to find the value of X. Hmm, let me... | Emma checked her car's odometer, which initially read \( X \) miles. After driving for 4 hours one day and 6 hours the next day, the odometer read 5310 miles. We know her average speed was 3 miles per hour. To find \( X \):
1. Calculate the total driving time: \( 4 \) hours + \( 6 \) hours = \( 10 \) hours.
2. Use the... | 966 | MetaMath-AIME | <think>
Okay, so Emma checked her car's odometer and it showed X miles. Then she drove for 4 hours one day and 6 hours the next day, and after that, the odometer reads 5310 miles. The question is asking for her average speed in miles per hour, and we already know the answer is 3. So, we need to find the value of X. Hmm... | [
{
"from": "human",
"value": "Emma checks her car's odometer which reads X miles. After a 4-hour drive today and 6 hours the next day, she sees that it now reads 5310 miles. What was her average speed in miles per hour? If we know the answer to the above question is 3, what is the value of unknown variable X... |
Ten boxes of chocolates cost less than $35.00 while X boxes cost more than $38.00. What is the cost of one box of chocolates? If we know the answer to the above question is 3.46, what is the value of unknown variable X? | To determine the value of X, we first need to understand the cost implications of the chocolates mentioned in the question. \n\n1. We know that ten boxes of chocolates cost less than $35.00. Let's denote the cost of one box of chocolates as \(C\). Therefore, we can write:\n 10C < 35 \n\n2. Dividing both sides of the ... | Okay, let's try to figure out this problem. So, we have ten boxes of chocolates costing less than $35.00, and X boxes costing more than $38.00. We need to find the cost of one box of chocolates, and they tell us the answer is $3.46. Then, we have to find the value of X. Hmm, let's take it step by step.
First, the prob... | Given that ten boxes of chocolates cost less than $35.00 and X boxes cost more than $38.00, we need to determine the value of X when the cost of one box of chocolates is $3.46.
First, we verify the cost of ten boxes:
\[
10 \times 3.46 = 34.60
\]
Since $34.60 is less than $35.00, this confirms the cost per box is corre... | 1,098 | MetaMath-AIME | <think>
Okay, let's try to figure out this problem. So, we have ten boxes of chocolates costing less than $35.00, and X boxes costing more than $38.00. We need to find the cost of one box of chocolates, and they tell us the answer is $3.46. Then, we have to find the value of X. Hmm, let's take it step by step.
First, ... | [
{
"from": "human",
"value": "Ten boxes of chocolates cost less than $35.00 while X boxes cost more than $38.00. What is the cost of one box of chocolates? If we know the answer to the above question is 3.46, what is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, l... |
If a conference call lasted for 2 hours and 50 minutes, how many minutes does that total? | To convert the conference call duration into minutes, we can break the time down into hours and minutes.
1. First, we know that 1 hour is equal to 60 minutes.
2. The conference call lasted 2 hours and 50 minutes.
3. We convert the hours into minutes: 2 hours × 60 minutes/hour = 120 minutes.
4. Now, we add the remaini... | Okay, let's see. The problem is asking to convert a conference call duration of 2 hours and 50 minutes into total minutes. Hmm, right. So, I need to figure out how many minutes are in 2 hours and then add the remaining 50 minutes to that.
First, I know that 1 hour is equal to 60 minutes. So, if the call lasted 2 hour... | To convert the duration of a conference call lasting 2 hours and 50 minutes into total minutes, we start by converting the hours into minutes.
1 hour is equal to 60 minutes, so 2 hours is:
\[
2 \text{ hours} \times 60 \text{ minutes/hour} = 120 \text{ minutes}
\]
Next, we add the remaining 50 minutes to the 120 minu... | 913 | MetaMath-AIME | <think>
Okay, let's see. The problem is asking to convert a conference call duration of 2 hours and 50 minutes into total minutes. Hmm, right. So, I need to figure out how many minutes are in 2 hours and then add the remaining 50 minutes to that.
First, I know that 1 hour is equal to 60 minutes. So, if the call laste... | [
{
"from": "human",
"value": "If a conference call lasted for 2 hours and 50 minutes, how many minutes does that total?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. The problem is asking to convert a conference call duration of 2 hours and 50 minutes into total minutes. Hmm, right. So... |
In a rectangular prism, Lucy tallied the number of faces, Lucas counted the edges, and Lily counted the vertices. What is the total sum of their counts? | In a rectangular prism, we can identify the following:
1. **Faces**: A rectangular prism has 6 faces. There are two faces for each dimension - front and back, left and right, top and bottom.
2. **Edges**: A rectangular prism has 12 edges. Each vertex connects edges along the three dimensions.
3. **Vertices**: A rect... | Okay, so I need to find the total sum of the number of faces, edges, and vertices that Lucy, Lucas, and Lily each counted on a rectangular prism. Let me think. First, I should recall what a rectangular prism is. It's a three-dimensional shape with six faces, all of which are rectangles. Right? So, like a box shape.
L... | Lucy counted the number of faces on a rectangular prism, which is 6. Lucas counted the number of edges, which is 12. Lily counted the number of vertices, which is 8.
To find the total sum of their counts, we add these numbers together:
\[
6 \text{ (faces)} + 12 \text{ (edges)} + 8 \text{ (vertices)} = 26
\]
We verif... | 1,135 | MetaMath-AIME | <think>
Okay, so I need to find the total sum of the number of faces, edges, and vertices that Lucy, Lucas, and Lily each counted on a rectangular prism. Let me think. First, I should recall what a rectangular prism is. It's a three-dimensional shape with six faces, all of which are rectangles. Right? So, like a box sh... | [
{
"from": "human",
"value": "In a rectangular prism, Lucy tallied the number of faces, Lucas counted the edges, and Lily counted the vertices. What is the total sum of their counts?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the total sum of the number of faces, edges, and v... |
What is the result of the expression $a + a(a^a)$ when $a$ is equal to 1? | To solve the expression $a + a(a^a)$ when $a = 1$, we will substitute 1 into the expression step by step:
1. Substitute $a = 1$ into the expression:
$$1 + 1(1^1)$$
2. Calculate $1^1$:
$$1^1 = 1$$
3. Substitute back into the expression:
$$1 + 1(1)$$
4. Now, multiply $1(1)$:
$$1 + 1 = 2$$... | Okay, let's see. I need to figure out the result of the expression a + a(a^a) when a is equal to 1. Hmm, let me break this down step by step. First, I should substitute the value of a into the expression. Since a is 1, I can replace every instance of a with 1.
So, the original expression is a + a(a^a). Substituting a ... | The expression \( a + a(a^a) \) when \( a = 1 \) is evaluated as follows:
1. Substitute \( a = 1 \):
\( 1 + 1(1^1) \).
2. Compute the exponent \( 1^1 \):
\( 1^1 = 1 \).
3. Perform the multiplication:
\( 1 \times 1 = 1 \).
4. Add the results:
\( 1 + 1 = 2 \).
**Answer:** \(\boxed{2}\) | 1,071 | MetaMath-AIME | <think>
Okay, let's see. I need to figure out the result of the expression a + a(a^a) when a is equal to 1. Hmm, let me break this down step by step. First, I should substitute the value of a into the expression. Since a is 1, I can replace every instance of a with 1.
So, the original expression is a + a(a^a). Substit... | [
{
"from": "human",
"value": "What is the result of the expression $a + a(a^a)$ when $a$ is equal to 1?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. I need to figure out the result of the expression a + a(a^a) when a is equal to 1. Hmm, let me break this down step by step. First, I sh... |
Sarah's bicycle travels at an average speed of 15 miles per hour while David's bicycle travels at X miles per hour. The combined average speed of Sarah and David, if both ride for the same amount of time, is 10. What is the value of the unknown variable X? | To solve this problem, we need to determine the value of X, which represents David's average speed in miles per hour.
Here's the step-by-step breakdown:
1. Let's denote Sarah's average speed as S = 15 miles per hour.
2. David's average speed is represented as X miles per hour.
3. When both Sarah and David ride for th... | Okay, let me try to figure out this problem. So, Sarah's bicycle has an average speed of 15 miles per hour, and David's is X miles per hour. The combined average speed when they both ride for the same amount of time is 10. I need to find X.
Hmm, average speed problems can sometimes be a bit tricky. Let me recall. If t... | Sarah's bicycle travels at an average speed of 15 miles per hour, and David's bicycle travels at \( X \) miles per hour. The combined average speed of Sarah and David, when both ride for the same amount of time, is 10. We need to find \( X \).
If both Sarah and David ride for \( t \) hours, the distance Sarah travels ... | 185 | MetaMath-AIME | <think>
Okay, let me try to figure out this problem. So, Sarah's bicycle has an average speed of 15 miles per hour, and David's is X miles per hour. The combined average speed when they both ride for the same amount of time is 10. I need to find X.
Hmm, average speed problems can sometimes be a bit tricky. Let me reca... | [
{
"from": "human",
"value": "Sarah's bicycle travels at an average speed of 15 miles per hour while David's bicycle travels at X miles per hour. The combined average speed of Sarah and David, if both ride for the same amount of time, is 10. What is the value of the unknown variable X?"
},
{
"from": ... |
Given that $m$ and $n$ are constants, and the equation $(x + 3)(x + m) = x^2 + nx + 9$ holds true, what is the value of $n$? | To solve the equation \((x + 3)(x + m) = x^2 + nx + 9\), we first expand the left-hand side:
\[(x + 3)(x + m) = x^2 + mx + 3x + 3m = x^2 + (m + 3)x + 3m.\]
Now, we can set the two sides of the equation equal to each other:
\[x^2 + (m + 3)x + 3m = x^2 + nx + 9.\]
Since both sides of the equation have the same lead... | Okay, so I need to solve for n in the equation (x + 3)(x + m) = x² + nx + 9. Hmm, let's start by expanding the left side of the equation.
First, I'll use the distributive property, also known as the FOIL method for multiplying two binomials. FOIL stands for First, Outer, Inner, Last, right? So, applying that here:
F... | To solve for \( n \) in the equation \((x + 3)(x + m) = x^2 + nx + 9\), we start by expanding the left side using the distributive property (FOIL method):
\[
(x + 3)(x + m) = x^2 + xm + 3x + 3m
\]
Combining the like terms \( xm \) and \( 3x \), we get:
\[
x^2 + (m + 3)x + 3m
\]
This expression must be equal to the ... | 154 | MetaMath-AIME | <think>
Okay, so I need to solve for n in the equation (x + 3)(x + m) = x² + nx + 9. Hmm, let's start by expanding the left side of the equation.
First, I'll use the distributive property, also known as the FOIL method for multiplying two binomials. FOIL stands for First, Outer, Inner, Last, right? So, applying that ... | [
{
"from": "human",
"value": "Given that $m$ and $n$ are constants, and the equation $(x + 3)(x + m) = x^2 + nx + 9$ holds true, what is the value of $n$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to solve for n in the equation (x + 3)(x + m) = x² + nx + 9. Hmm, let's start by expan... |
Considering that $d = 5$, what is the largest number in the set \{ -d, 3d, \frac {45}{d}, d^2, 4 \}, where the options are \text{(A)} -d, \text{(B)} 3d, \text{(C)} \frac {45}{d}, \text{(D)} d^2, \text{(E)} 4? | Given that \( d = 5 \), we can compute the values in the set \{ -d, 3d, \frac{45}{d}, d^2, 4 \} as follows:
1. **Calculate each expression**:
- \( -d = -5 \)
- \( 3d = 3 \times 5 = 15 \)
- \( \frac{45}{d} = \frac{45}{5} = 9 \)
- \( d^2 = 5^2 = 25 \)
- \( 4 = 4 \) (remains as is)
2. **List the calculate... | Okay, so the problem is asking for the largest number in the set \{ -d, 3d, 45/d, d², 4 \}, where d is given as 5. The options are labeled from A to E, each corresponding to one of the numbers in the set. Let me try to figure this out step by step.
First, I need to substitute d = 5 into each element of the set. Let me... | Given \( d = 5 \), we need to determine the largest number in the set \{ -d, 3d, \frac{45}{d}, d^2, 4 \}.
1. Substitute \( d = 5 \) into each element of the set:
- \(-d = -5\)
- \(3d = 3 \times 5 = 15\)
- \(\frac{45}{d} = \frac{45}{5} = 9\)
- \(d^2 = 5^2 = 25\)
- \(4 = 4\)
2. The set becomes \{ -5, 15,... | 881 | MetaMath-AIME | <think>
Okay, so the problem is asking for the largest number in the set \{ -d, 3d, 45/d, d², 4 \}, where d is given as 5. The options are labeled from A to E, each corresponding to one of the numbers in the set. Let me try to figure this out step by step.
First, I need to substitute d = 5 into each element of the set... | [
{
"from": "human",
"value": "Considering that $d = 5$, what is the largest number in the set \\{ -d, 3d, \\frac {45}{d}, d^2, 4 \\}, where the options are \\text{(A)} -d, \\text{(B)} 3d, \\text{(C)} \\frac {45}{d}, \\text{(D)} d^2, \\text{(E)} 4?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so ... |
If a bakery sells 10 croissants for every 6 danishes and anticipates selling 60 croissants next week, how many danishes should it expect to sell? | 1. We start by noting the ratio of croissants to danishes from the bakery, which is 10:6.
2. To simplify this ratio, we can divide both numbers by their greatest common divisor, which is 2:
\[ 10:6 = 5:3 \]
3. This means that for every 5 croissants sold, 3 danishes are sold.
4. Now, we know that the bakery a... | Okay, let me try to figure out this problem. So, the bakery sells 10 croissants for every 6 danishes. Hmm, so that's like a ratio, right? 10 croissants to 6 danishes. They want to know how many danishes they should expect to sell next week if they anticipate selling 60 croissants.
First, let me write down the ratio t... | The bakery's sales ratio is 10 croissants to 6 danishes, which simplifies to 5:3. To find the expected number of danishes when selling 60 croissants:
1. **Set up the proportion** based on the ratio:
\[
\frac{10 \text{ croissants}}{6 \text{ danishes}} = \frac{60 \text{ croissants}}{x \text{ danishes}}
\]
2... | 578 | MetaMath-AIME | <think>
Okay, let me try to figure out this problem. So, the bakery sells 10 croissants for every 6 danishes. Hmm, so that's like a ratio, right? 10 croissants to 6 danishes. They want to know how many danishes they should expect to sell next week if they anticipate selling 60 croissants.
First, let me write down the... | [
{
"from": "human",
"value": "If a bakery sells 10 croissants for every 6 danishes and anticipates selling 60 croissants next week, how many danishes should it expect to sell?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let me try to figure out this problem. So, the bakery sells 10 croissants f... |
Michael is brewing iced tea. His formula requires 3 times as much water as tea and X times as much tea as sugar. He uses 1 cup of sugar. He needs 15 cups of water. What is the value of the unknown variable X? | To solve this problem, let's analyze the information provided step by step.
1. The formula requires 3 times as much water as tea. We know he uses 15 cups of water.
Therefore, the amount of tea used is:
\[ \text{Tea} = \frac{\text{Water}}{3} = \frac{15}{3} = 5 \text{ cups} \]
2. The formula states that there is ... | Okay, let's see. Michael is making iced tea, and there's some formula he follows. The problem says he uses 3 times as much water as tea. Hmm, so if I let the amount of tea be something, then the water would be three times that. Then it also says he uses X times as much tea as sugar. And he uses 1 cup of sugar. They wan... | Michael uses 1 cup of sugar. According to the problem, the amount of tea he uses is \( X \) times the amount of sugar. Therefore, the amount of tea is \( X \) cups. The problem also states that the amount of water used is 3 times the amount of tea. This means the amount of water is \( 3X \) cups. Given that he needs 15... | 671 | MetaMath-AIME | <think>
Okay, let's see. Michael is making iced tea, and there's some formula he follows. The problem says he uses 3 times as much water as tea. Hmm, so if I let the amount of tea be something, then the water would be three times that. Then it also says he uses X times as much tea as sugar. And he uses 1 cup of sugar. ... | [
{
"from": "human",
"value": "Michael is brewing iced tea. His formula requires 3 times as much water as tea and X times as much tea as sugar. He uses 1 cup of sugar. He needs 15 cups of water. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. M... |
Hillcrest School has 950 students. Each student takes 3 classes each day. Each teacher teaches X classes. Each class has 25 students. There are 19 teachers working at Hillcrest School. What is the value of the unknown variable X? | To solve this problem, let's break down the information given step by step.
1. **Total number of students**: 950 students
2. **Classes taken by each student per day**: 3 classes
3. **Total number of classes taken by all students**: Since each student takes 3 classes, the total number of classes taken will be the numbe... | Okay, so Hillcrest School has 950 students, and each student takes 3 classes every day. Each teacher teaches X classes, and each class has 25 students. There are 19 teachers. I need to find the value of X. Hmm, let me think step by step.
First, maybe I should figure out how many total class enrollments there are. Sinc... | Hillcrest School has 950 students, each taking 3 classes per day. To find the total number of class enrollments, we multiply the number of students by the number of classes each student takes:
\[
950 \text{ students} \times 3 \text{ classes/student} = 2850 \text{ class enrollments}
\]
Each class has 25 students, so t... | 1,128 | MetaMath-AIME | <think>
Okay, so Hillcrest School has 950 students, and each student takes 3 classes every day. Each teacher teaches X classes, and each class has 25 students. There are 19 teachers. I need to find the value of X. Hmm, let me think step by step.
First, maybe I should figure out how many total class enrollments there a... | [
{
"from": "human",
"value": "Hillcrest School has 950 students. Each student takes 3 classes each day. Each teacher teaches X classes. Each class has 25 students. There are 19 teachers working at Hillcrest School. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think... |
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