Blame for attack_sets/word_problems/dev.jsonl

{"instruction": "On a number line, a robot's stopping point after a command with parameter p is 3*p - 20. For which parameter p does the robot stop at -44? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -8", "id": "algebra-L1-18097c992e23b8b26ff5-word", "source_id": "algebra-18097c992e23b8b26ff5", "topic": "algebra", "level": 1, "kind": "solve", "question": "On a number line, a robot's stopping point after a command with parameter p is 3*p - 20. For which parameter p does the robot stop at -44?", "answer": "-8", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L1-18097c992e23b8b26ff5", "attack": "word_problem", "target": "algebra", "question_original": "Solve 3*x - 20 = -44 for x.", "variable": "p", "underlying_expression": "3*p - 20 = -44", "answer_in_variable": "-8", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "A spring scale shows 4*s - 20 grams when its slider sits s notches from the centre mark (notches left of centre count as negative). Find s when the scale shows 28 grams. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 12", "id": "algebra-L1-eea1f2cae2f06678530a-word", "source_id": "algebra-eea1f2cae2f06678530a", "topic": "algebra", "level": 1, "kind": "solve", "question": "A spring scale shows 4*s - 20 grams when its slider sits s notches from the centre mark (notches left of centre count as negative). Find s when the scale shows 28 grams.", "answer": "12", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L1-eea1f2cae2f06678530a", "attack": "word_problem", "target": "algebra", "question_original": "Solve 4*x - 20 = 28 for x.", "variable": "s", "underlying_expression": "4*s - 20 = 28", "answer_in_variable": "12", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "The elevation of a hiking marker, in meters relative to a lake surface, is -9*m - 4, where m is the marker's index counted from the trailhead (markers before the trailhead have negative index). Which marker m is at elevation 50? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -6", "id": "algebra-L1-02ed2084d5de4eed6cfd-word", "source_id": "algebra-02ed2084d5de4eed6cfd", "topic": "algebra", "level": 1, "kind": "solve", "question": "The elevation of a hiking marker, in meters relative to a lake surface, is -9*m - 4, where m is the marker's index counted from the trailhead (markers before the trailhead have negative index). Which marker m is at elevation 50?", "answer": "-6", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L1-02ed2084d5de4eed6cfd", "attack": "word_problem", "target": "algebra", "question_original": "Solve -9*x - 4 = 50 for x.", "variable": "m", "underlying_expression": "-9*m - 4 = 50", "answer_in_variable": "-6", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "An oven program sets the temperature to 7*w - 20 degrees above its base setting when the dial is turned w clicks (counter-clockwise clicks are negative). How many clicks w give -13 degrees above base? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 1", "id": "algebra-L1-dcec9caffcb37b11668f-word", "source_id": "algebra-dcec9caffcb37b11668f", "topic": "algebra", "level": 1, "kind": "solve", "question": "An oven program sets the temperature to 7*w - 20 degrees above its base setting when the dial is turned w clicks (counter-clockwise clicks are negative). How many clicks w give -13 degrees above base?", "answer": "1", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L1-dcec9caffcb37b11668f", "attack": "word_problem", "target": "algebra", "question_original": "Solve 7*x - 20 = -13 for x.", "variable": "w", "underlying_expression": "7*w - 20 = -13", "answer_in_variable": "1", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "A stock's price change, in cents, t days after a news release is predicted to be 7*t - 5, where negative t refers to days before the release. On which day t is the predicted change 30 cents? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 5", "id": "algebra-L1-f621eb27efae07c11362-word", "source_id": "algebra-f621eb27efae07c11362", "topic": "algebra", "level": 1, "kind": "solve", "question": "A stock's price change, in cents, t days after a news release is predicted to be 7*t - 5, where negative t refers to days before the release. On which day t is the predicted change 30 cents?", "answer": "5", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L1-f621eb27efae07c11362", "attack": "word_problem", "target": "algebra", "question_original": "Solve 7*x - 5 = 30 for x.", "variable": "t", "underlying_expression": "7*t - 5 = 30", "answer_in_variable": "5", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "In a board game, a player's score after landing on square n is 3*n + 9 points; squares behind the start are numbered negatively. Which square n yields a score of -12 points? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -7", "id": "algebra-L1-bb3b075ffb30a6067aa6-word", "source_id": "algebra-bb3b075ffb30a6067aa6", "topic": "algebra", "level": 1, "kind": "solve", "question": "In a board game, a player's score after landing on square n is 3*n + 9 points; squares behind the start are numbered negatively. Which square n yields a score of -12 points?", "answer": "-7", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L1-bb3b075ffb30a6067aa6", "attack": "word_problem", "target": "algebra", "question_original": "Solve 3*x + 9 = -12 for x.", "variable": "n", "underlying_expression": "3*n + 9 = -12", "answer_in_variable": "-7", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "A drone's altitude, in meters relative to a rooftop, is 5*z - 2 when its control lever is at position z (pulling the lever back gives negative z). Find the lever position z that puts the drone at 38 meters. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 8", "id": "algebra-L1-b08572e85e15d4ad9877-word", "source_id": "algebra-b08572e85e15d4ad9877", "topic": "algebra", "level": 1, "kind": "solve", "question": "A drone's altitude, in meters relative to a rooftop, is 5*z - 2 when its control lever is at position z (pulling the lever back gives negative z). Find the lever position z that puts the drone at 38 meters.", "answer": "8", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L1-b08572e85e15d4ad9877", "attack": "word_problem", "target": "algebra", "question_original": "Solve 5*x - 2 = 38 for x.", "variable": "z", "underlying_expression": "5*z - 2 = 38", "answer_in_variable": "8", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "An electrician measures 6*u - 11 volts on a test circuit when the offset knob is at setting u (u can be negative). What knob setting u gives -47 volts? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -6", "id": "algebra-L1-83ad5b606c55a43ee046-word", "source_id": "algebra-83ad5b606c55a43ee046", "topic": "algebra", "level": 1, "kind": "solve", "question": "An electrician measures 6*u - 11 volts on a test circuit when the offset knob is at setting u (u can be negative). What knob setting u gives -47 volts?", "answer": "-6", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L1-83ad5b606c55a43ee046", "attack": "word_problem", "target": "algebra", "question_original": "Solve 6*x - 11 = -47 for x.", "variable": "u", "underlying_expression": "6*u - 11 = -47", "answer_in_variable": "-6", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "A cyclist's net gain in height, in meters, after riding r laps of a hilly loop is -4*r - 11; riding the loop backwards counts as negative r. For which r is the net gain 13 meters? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -6", "id": "algebra-L1-467e356fb80588af0ba4-word", "source_id": "algebra-467e356fb80588af0ba4", "topic": "algebra", "level": 1, "kind": "solve", "question": "A cyclist's net gain in height, in meters, after riding r laps of a hilly loop is -4*r - 11; riding the loop backwards counts as negative r. For which r is the net gain 13 meters?", "answer": "-6", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L1-467e356fb80588af0ba4", "attack": "word_problem", "target": "algebra", "question_original": "Solve -4*x - 11 = 13 for x.", "variable": "r", "underlying_expression": "-4*r - 11 = 13", "answer_in_variable": "-6", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "A warehouse's net inventory change after q shipments is 5*q - 16 boxes, where returned shipments count as negative q. Find q when the net change is -51 boxes. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -7", "id": "algebra-L1-767e21d1023e987361a8-word", "source_id": "algebra-767e21d1023e987361a8", "topic": "algebra", "level": 1, "kind": "solve", "question": "A warehouse's net inventory change after q shipments is 5*q - 16 boxes, where returned shipments count as negative q. Find q when the net change is -51 boxes.", "answer": "-7", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L1-767e21d1023e987361a8", "attack": "word_problem", "target": "algebra", "question_original": "Solve 5*x - 16 = -51 for x.", "variable": "q", "underlying_expression": "5*q - 16 = -51", "answer_in_variable": "-7", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "An engineer writes the power of a circuit at setting k as (14*k + 18)*(k - 46) watts. Expand the product so that the formula has no parentheses. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 14*x**2 - 626*x - 828", "id": "algebra-L2-bd7456a2d0da18ce57ec-word", "source_id": "algebra-bd7456a2d0da18ce57ec", "topic": "algebra", "level": 2, "kind": "algebra", "question": "An engineer writes the power of a circuit at setting k as (14*k + 18)*(k - 46) watts. Expand the product so that the formula has no parentheses.", "answer": "14*x**2 - 626*x - 828", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L2-bd7456a2d0da18ce57ec", "attack": "word_problem", "target": "algebra", "question_original": "Expand (14*x + 18)*(x - 46).", "variable": "k", "underlying_expression": "(14*k + 18)*(k - 46)", "answer_in_variable": "14*k**2 - 626*k - 828", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "A puzzle asks for the whole numbers n for which 8*n**2 - 232*n - 768 = 0. Find all solutions n and list them in increasing order. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: [-3, 32]", "id": "algebra-L2-6bfac99be17a56797b42-word", "source_id": "algebra-6bfac99be17a56797b42", "topic": "algebra", "level": 2, "kind": "quadratic", "question": "A puzzle asks for the whole numbers n for which 8*n**2 - 232*n - 768 = 0. Find all solutions n and list them in increasing order.", "answer": "[-3, 32]", "expr": "8*x**2 - 232*x - 768", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L2-6bfac99be17a56797b42", "attack": "word_problem", "target": "algebra", "question_original": "Solve 8*x**2 - 232*x - 768 = 0 for x. List all roots in increasing order.", "variable": "n", "underlying_expression": "8*n**2 - 232*n - 768 = 0", "answer_in_variable": "[-3, 32]", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "The area of a picture frame, in square inches, is (-9*s - 47)*(s + 47), where s is a border width in inches. Write this area in expanded form. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -9*x**2 - 470*x - 2209", "id": "algebra-L2-013471956ab0a066a43b-word", "source_id": "algebra-013471956ab0a066a43b", "topic": "algebra", "level": 2, "kind": "algebra", "question": "The area of a picture frame, in square inches, is (-9*s - 47)*(s + 47), where s is a border width in inches. Write this area in expanded form.", "answer": "-9*x**2 - 470*x - 2209", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L2-013471956ab0a066a43b", "attack": "word_problem", "target": "algebra", "question_original": "Expand (-9*x - 47)*(x + 47).", "variable": "s", "underlying_expression": "(-9*s - 47)*(s + 47)", "answer_in_variable": "-9*s**2 - 470*s - 2209", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "A farmer computes the yield of a field as (3*m - 45)*(m + 4) kilograms when m extra rows are planted. Expand the expression into a polynomial in m. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 3*x**2 - 33*x - 180", "id": "algebra-L2-6dff946c50b96b48759d-word", "source_id": "algebra-6dff946c50b96b48759d", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A farmer computes the yield of a field as (3*m - 45)*(m + 4) kilograms when m extra rows are planted. Expand the expression into a polynomial in m.", "answer": "3*x**2 - 33*x - 180", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L2-6dff946c50b96b48759d", "attack": "word_problem", "target": "algebra", "question_original": "Expand (3*x - 45)*(x + 4).", "variable": "m", "underlying_expression": "(3*m - 45)*(m + 4)", "answer_in_variable": "3*m**2 - 33*m - 180", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "A radar tracker reports that an object is at ground level when 4*s**2 - 320*s + 6364 = 0, where s is the time in seconds relative to the radar ping (negative s is before the ping). Find all such times s in increasing order. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: [37, 43]", "id": "algebra-L2-8890db8366e6885a7df0-word", "source_id": "algebra-8890db8366e6885a7df0", "topic": "algebra", "level": 2, "kind": "quadratic", "question": "A radar tracker reports that an object is at ground level when 4*s**2 - 320*s + 6364 = 0, where s is the time in seconds relative to the radar ping (negative s is before the ping). Find all such times s in increasing order.", "answer": "[37, 43]", "expr": "4*x**2 - 320*x + 6364", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L2-8890db8366e6885a7df0", "attack": "word_problem", "target": "algebra", "question_original": "Solve 4*x**2 - 320*x + 6364 = 0 for x. List all roots in increasing order.", "variable": "s", "underlying_expression": "4*s**2 - 320*s + 6364 = 0", "answer_in_variable": "[37, 43]", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "A tank's cross-sectional area, in square meters, is (-5*w - 22)*(w + 18), where w is a width offset in meters. Rewrite the area in standard form by multiplying it out. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -5*x**2 - 112*x - 396", "id": "algebra-L2-2d5123265d5e227ee5c0-word", "source_id": "algebra-2d5123265d5e227ee5c0", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A tank's cross-sectional area, in square meters, is (-5*w - 22)*(w + 18), where w is a width offset in meters. Rewrite the area in standard form by multiplying it out.", "answer": "-5*x**2 - 112*x - 396", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L2-2d5123265d5e227ee5c0", "attack": "word_problem", "target": "algebra", "question_original": "Expand (-5*x - 22)*(x + 18).", "variable": "w", "underlying_expression": "(-5*w - 22)*(w + 18)", "answer_in_variable": "-5*w**2 - 112*w - 396", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "A company's profit at production level p is (7*p + 34)*(p - 2) dollars. Expand the profit formula completely. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 7*x**2 + 20*x - 68", "id": "algebra-L2-8c8b8e6effcd3ba04f29-word", "source_id": "algebra-8c8b8e6effcd3ba04f29", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A company's profit at production level p is (7*p + 34)*(p - 2) dollars. Expand the profit formula completely.", "answer": "7*x**2 + 20*x - 68", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L2-8c8b8e6effcd3ba04f29", "attack": "word_problem", "target": "algebra", "question_original": "Expand (7*x + 34)*(x - 2).", "variable": "p", "underlying_expression": "(7*p + 34)*(p - 2)", "answer_in_variable": "7*p**2 + 20*p - 68", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "In a pricing study, the revenue difference between two plans is zero when 3*p**2 + 213*p + 3720 = 0, where p is the price change in dollars (negative for discounts). Find all values of p, listed from smallest to largest. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: [-40, -31]", "id": "algebra-L2-a41a9655d04e3491b6ab-word", "source_id": "algebra-a41a9655d04e3491b6ab", "topic": "algebra", "level": 2, "kind": "quadratic", "question": "In a pricing study, the revenue difference between two plans is zero when 3*p**2 + 213*p + 3720 = 0, where p is the price change in dollars (negative for discounts). Find all values of p, listed from smallest to largest.", "answer": "[-40, -31]", "expr": "3*x**2 + 213*x + 3720", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L2-a41a9655d04e3491b6ab", "attack": "word_problem", "target": "algebra", "question_original": "Solve 3*x**2 + 213*x + 3720 = 0 for x. List all roots in increasing order.", "variable": "p", "underlying_expression": "3*p**2 + 213*p + 3720 = 0", "answer_in_variable": "[-40, -31]", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "A physics lab models the energy stored in a system at setting k as k**2 + 44*k + 403 joules. Express this model as a product of irreducible factors with integer coefficients. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (x + 13)*(x + 31)", "id": "algebra-L2-f6658ce90c22f4749bf2-word", "source_id": "algebra-f6658ce90c22f4749bf2", "topic": "algebra", "level": 2, "kind": "factor", "question": "A physics lab models the energy stored in a system at setting k as k**2 + 44*k + 403 joules. Express this model as a product of irreducible factors with integer coefficients.", "answer": "(x + 13)*(x + 31)", "expr": "x**2 + 44*x + 403", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L2-f6658ce90c22f4749bf2", "attack": "word_problem", "target": "algebra", "question_original": "Factor x**2 + 44*x + 403 over the integers.", "variable": "k", "underlying_expression": "k**2 + 44*k + 403", "answer_in_variable": "(k + 13)*(k + 31)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "The volume of a container, in cubic centimeters, works out to 3*s**2 + 228*s + 4089 for a design parameter s. Factor the expression fully, using integer coefficients. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 3*(x + 29)*(x + 47)", "id": "algebra-L2-e5098c8cae79fdabd8ec-word", "source_id": "algebra-e5098c8cae79fdabd8ec", "topic": "algebra", "level": 2, "kind": "factor", "question": "The volume of a container, in cubic centimeters, works out to 3*s**2 + 228*s + 4089 for a design parameter s. Factor the expression fully, using integer coefficients.", "answer": "3*(x + 29)*(x + 47)", "expr": "3*x**2 + 228*x + 4089", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L2-e5098c8cae79fdabd8ec", "attack": "word_problem", "target": "algebra", "question_original": "Factor 3*x**2 + 228*x + 4089 over the integers.", "variable": "s", "underlying_expression": "3*s**2 + 228*s + 4089", "answer_in_variable": "3*(s + 29)*(s + 47)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "An economist's ratio of total revenue to the number of batches is (2*k**2 - 3*k - 464)/(k - 16), with k a pricing parameter. Simplify the ratio into a polynomial in k, valid wherever it is defined. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 2*x + 29", "id": "algebra-L3-a12b7b177ec8ac795606-word", "source_id": "algebra-a12b7b177ec8ac795606", "topic": "algebra", "level": 3, "kind": "simplify", "question": "An economist's ratio of total revenue to the number of batches is (2*k**2 - 3*k - 464)/(k - 16), with k a pricing parameter. Simplify the ratio into a polynomial in k, valid wherever it is defined.", "answer": "2*x + 29", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L3-a12b7b177ec8ac795606", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (2*x**2 - 3*x - 464)/(x - (16)) for x != 16.", "variable": "k", "underlying_expression": "(2*k**2 - 3*k - 464)/(k - 16)", "answer_in_variable": "2*k + 29", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "The height of a rectangular panel, in centimeters, equals its area divided by its width, which gives (10*s**2 + 260*s)/(s + 26) for a size parameter s. Simplify this expression to a polynomial in s for all allowed s. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 10*x", "id": "algebra-L3-cb20fc94769161be8b4d-word", "source_id": "algebra-cb20fc94769161be8b4d", "topic": "algebra", "level": 3, "kind": "simplify", "question": "The height of a rectangular panel, in centimeters, equals its area divided by its width, which gives (10*s**2 + 260*s)/(s + 26) for a size parameter s. Simplify this expression to a polynomial in s for all allowed s.", "answer": "10*x", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L3-cb20fc94769161be8b4d", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (10*x**2 + 260*x)/(x - (-26)) for x != -26.", "variable": "s", "underlying_expression": "(10*s**2 + 260*s)/(s + 26)", "answer_in_variable": "10*s", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "Two weights on a balance beam sit at positions x and y (in decimeters from the pivot, negative on the left). The equilibrium conditions give -1*x + 1*y = -7 and 1*x - 2*y = 14. Find the positions as (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (0, -7)", "id": "algebra-L3-82d1fb833d93da836756-word", "source_id": "algebra-82d1fb833d93da836756", "topic": "algebra", "level": 3, "kind": "solve", "question": "Two weights on a balance beam sit at positions x and y (in decimeters from the pivot, negative on the left). The equilibrium conditions give -1*x + 1*y = -7 and 1*x - 2*y = 14. Find the positions as (x, y).", "answer": "(0, -7)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L3-82d1fb833d93da836756", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: -1*x + 1*y = -7, 1*x - 2*y = 14 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "-1*x + 1*y = -7, 1*x - 2*y = 14", "answer_in_variable": "(0, -7)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "A chemist's concentration formula is (9*m**2 - 437*m + 240)/(m - 48) grams per liter, where m is a mixing parameter. Simplify the formula to a polynomial in m (assume the denominator is not zero). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 9*x - 5", "id": "algebra-L3-a95d9f10b72d4734e8a0-word", "source_id": "algebra-a95d9f10b72d4734e8a0", "topic": "algebra", "level": 3, "kind": "simplify", "question": "A chemist's concentration formula is (9*m**2 - 437*m + 240)/(m - 48) grams per liter, where m is a mixing parameter. Simplify the formula to a polynomial in m (assume the denominator is not zero).", "answer": "9*x - 5", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L3-a95d9f10b72d4734e8a0", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (9*x**2 - 437*x + 240)/(x - (48)) for x != 48.", "variable": "m", "underlying_expression": "(9*m**2 - 437*m + 240)/(m - 48)", "answer_in_variable": "9*m - 5", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "A chemist adjusts the charges x and y of two ions in a model (charges may be negative or zero); the model's constraints are -2*x + 2*y = 12 and -3*x + 4*y = 23. Find the charges as an ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (-1, 5)", "id": "algebra-L3-622d89e7a373a638ad2d-word", "source_id": "algebra-622d89e7a373a638ad2d", "topic": "algebra", "level": 3, "kind": "solve", "question": "A chemist adjusts the charges x and y of two ions in a model (charges may be negative or zero); the model's constraints are -2*x + 2*y = 12 and -3*x + 4*y = 23. Find the charges as an ordered pair (x, y).", "answer": "(-1, 5)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L3-622d89e7a373a638ad2d", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: -2*x + 2*y = 12, -3*x + 4*y = 23 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "-2*x + 2*y = 12, -3*x + 4*y = 23", "answer_in_variable": "(-1, 5)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "The average cost per crate in a shipment, in dollars, is (12*x**2 - 297*x + 483)/(x - 23), where x is a design parameter. Simplify this expression to a polynomial in x, wherever it is defined. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 12*x - 21", "id": "algebra-L3-fb74d59a0671181155c6-word", "source_id": "algebra-fb74d59a0671181155c6", "topic": "algebra", "level": 3, "kind": "simplify", "question": "The average cost per crate in a shipment, in dollars, is (12*x**2 - 297*x + 483)/(x - 23), where x is a design parameter. Simplify this expression to a polynomial in x, wherever it is defined.", "answer": "12*x - 21", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L3-fb74d59a0671181155c6", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (12*x**2 - 297*x + 483)/(x - (23)) for x != 23.", "variable": "x", "underlying_expression": "(12*x**2 - 297*x + 483)/(x - 23)", "answer_in_variable": "12*x - 21", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "The scores x and y awarded in two rounds of a quiz (penalties can make a score negative or zero) satisfy 3*x - 3*y = -15 and 6*x + 4*y = -60. Find the ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (-8, -3)", "id": "algebra-L3-3f9f3e9ba41fc84486e9-word", "source_id": "algebra-3f9f3e9ba41fc84486e9", "topic": "algebra", "level": 3, "kind": "solve", "question": "The scores x and y awarded in two rounds of a quiz (penalties can make a score negative or zero) satisfy 3*x - 3*y = -15 and 6*x + 4*y = -60. Find the ordered pair (x, y).", "answer": "(-8, -3)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L3-3f9f3e9ba41fc84486e9", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 3*x - 3*y = -15, 6*x + 4*y = -60 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "3*x - 3*y = -15, 6*x + 4*y = -60", "answer_in_variable": "(-8, -3)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "Two thermometers are being calibrated. If x and y are the corrections (in degrees, possibly negative) for the first and second thermometer, the test readings give -3*x + 1*y = 28 and -5*x + 5*y = 50. Find the corrections as an ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (-9, 1)", "id": "algebra-L3-077a2e1a773f43e6fda7-word", "source_id": "algebra-077a2e1a773f43e6fda7", "topic": "algebra", "level": 3, "kind": "solve", "question": "Two thermometers are being calibrated. If x and y are the corrections (in degrees, possibly negative) for the first and second thermometer, the test readings give -3*x + 1*y = 28 and -5*x + 5*y = 50. Find the corrections as an ordered pair (x, y).", "answer": "(-9, 1)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L3-077a2e1a773f43e6fda7", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: -3*x + 1*y = 28, -5*x + 5*y = 50 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "-3*x + 1*y = 28, -5*x + 5*y = 50", "answer_in_variable": "(-9, 1)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "A machine's output rate is recorded as (4*t**2 - 58*t - 170)/(t - 17) units per hour, where t is the operating temperature setting. Simplify the rate to a polynomial in t, assuming the denominator is nonzero. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 4*x + 10", "id": "algebra-L3-7e7e923eefadae87e2d7-word", "source_id": "algebra-7e7e923eefadae87e2d7", "topic": "algebra", "level": 3, "kind": "simplify", "question": "A machine's output rate is recorded as (4*t**2 - 58*t - 170)/(t - 17) units per hour, where t is the operating temperature setting. Simplify the rate to a polynomial in t, assuming the denominator is nonzero.", "answer": "4*x + 10", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L3-7e7e923eefadae87e2d7", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (4*x**2 - 58*x - 170)/(x - (17)) for x != 17.", "variable": "t", "underlying_expression": "(4*t**2 - 58*t - 170)/(t - 17)", "answer_in_variable": "4*t + 10", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}
{"instruction": "A robot moves x meters east and y meters north (negative values mean west or south). Its sensors record -2*x - 6*y = -28 and -4*x - 2*y = -6. Find the ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (-1, 5)", "id": "algebra-L3-fd545ad19815411737b1-word", "source_id": "algebra-fd545ad19815411737b1", "topic": "algebra", "level": 3, "kind": "solve", "question": "A robot moves x meters east and y meters north (negative values mean west or south). Its sensors record -2*x - 6*y = -28 and -4*x - 2*y = -6. Find the ordered pair (x, y).", "answer": "(-1, 5)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "dev", "parent_id": "algebra-L3-fd545ad19815411737b1", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: -2*x - 6*y = -28, -4*x - 2*y = -6 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "-2*x - 6*y = -28, -4*x - 2*y = -6", "answer_in_variable": "(-1, 5)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"}