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raw_tmpl/tp_tp0cd_1791583347_00051.jsonl
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raw_tmpl/tp_tp0cd_1791583347_00052.jsonl
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $3.49/gallon and Premium at $5.08/gallon. A customer buys a mixture of both grades totaling 13 gallons for a combined cost of $54.91. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 13\n3.49r + 5.08p = 54.91\nr = 13 - p\n3.49(13 - p) + 5.08p = 54.91\n45.37 - 3.49p + 5.08p = 54.91\n1.59p = 54.91 - 45.37\n1.59p = 9.54\np = 9.54 / 1.59\np = 6\n#### 6", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: At a local gas station, Regular gasoline costs $2.57/gallon and Premium costs $3.57/gallon. A customer purchased a total of 12 gallons of both grades for $42.44. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 12\n2.57r + 3.57p = 42.44\nr = 12 - p\n2.57(12 - p) + 3.57p = 42.44\n30.84 - 2.57p + 3.57p = 42.44\n1.00p = 42.44 - 30.84\n1.00p = 11.60\np = 11.60 / 1.00\np = 58/5\n#### 58/5", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: At a local gas station, Regular gasoline costs $3.16/gallon and Premium costs $4.73/gallon. A customer purchased a total of 17 gallons of both grades for $61.57. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 17\n3.16r + 4.73p = 61.57\nr = 17 - p\n3.16(17 - p) + 4.73p = 61.57\n53.72 - 3.16p + 4.73p = 61.57\n1.57p = 61.57 - 53.72\n1.57p = 7.85\np = 7.85 / 1.57\np = 5\n#### 5", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: At a local gas station, Regular gasoline costs $3.13/gallon and Premium costs $5.06/gallon. A customer purchased a total of 21 gallons of both grades for $94.68. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 21\n3.13r + 5.06p = 94.68\nr = 21 - p\n3.13(21 - p) + 5.06p = 94.68\n65.73 - 3.13p + 5.06p = 94.68\n1.93p = 94.68 - 65.73\n1.93p = 28.95\np = 28.95 / 1.93\np = 15\n#### 15", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $3.03/gallon and Premium at $3.80/gallon. A customer buys a mixture of both grades totaling 29 gallons for a combined cost of $105.58. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 29\n3.03r + 3.80p = 105.58\nr = 29 - p\n3.03(29 - p) + 3.80p = 105.58\n87.87 - 3.03p + 3.80p = 105.58\n0.77p = 105.58 - 87.87\n0.77p = 17.71\np = 17.71 / 0.77\np = 23\n#### 23", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: At a local gas station, Regular gasoline costs $3.11/gallon and Premium costs $4.63/gallon. A customer purchased a total of 27 gallons of both grades for $111.90. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 27\n3.11r + 4.63p = 111.90\nr = 27 - p\n3.11(27 - p) + 4.63p = 111.90\n83.97 - 3.11p + 4.63p = 111.90\n1.52p = 111.90 - 83.97\n1.52p = 27.93\np = 27.93 / 1.52\np = 147/8\n#### 147/8", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $2.94/gallon and Premium at $3.58/gallon. A customer buys a mixture of both grades totaling 17 gallons for a combined cost of $50.62. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 17\n2.94r + 3.58p = 50.62\nr = 17 - p\n2.94(17 - p) + 3.58p = 50.62\n49.98 - 2.94p + 3.58p = 50.62\n0.64p = 50.62 - 49.98\n0.64p = 0.64\np = 0.64 / 0.64\np = 1\n#### 1", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $2.54/gallon and Premium at $3.48/gallon. A customer buys a mixture of both grades totaling 19 gallons for a combined cost of $55.31. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 19\n2.54r + 3.48p = 55.31\nr = 19 - p\n2.54(19 - p) + 3.48p = 55.31\n48.26 - 2.54p + 3.48p = 55.31\n0.94p = 55.31 - 48.26\n0.94p = 7.05\np = 7.05 / 0.94\np = 15/2\n#### 15/2", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $3.16/gallon and Premium at $4.79/gallon. A customer buys a mixture of both grades totaling 20 gallons for a combined cost of $69.72. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 20\n3.16r + 4.79p = 69.72\nr = 20 - p\n3.16(20 - p) + 4.79p = 69.72\n63.20 - 3.16p + 4.79p = 69.72\n1.63p = 69.72 - 63.20\n1.63p = 6.52\np = 6.52 / 1.63\np = 4\n#### 4", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: At a local gas station, Regular gasoline costs $2.73/gallon and Premium costs $3.26/gallon. A customer purchased a total of 25 gallons of both grades for $80.97. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 25\n2.73r + 3.26p = 80.97\nr = 25 - p\n2.73(25 - p) + 3.26p = 80.97\n68.25 - 2.73p + 3.26p = 80.97\n0.53p = 80.97 - 68.25\n0.53p = 12.72\np = 12.72 / 0.53\np = 24\n#### 24", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: At a local gas station, Regular gasoline costs $3.35/gallon and Premium costs $4.48/gallon. A customer purchased a total of 27 gallons of both grades for $106.27. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 27\n3.35r + 4.48p = 106.27\nr = 27 - p\n3.35(27 - p) + 4.48p = 106.27\n90.45 - 3.35p + 4.48p = 106.27\n1.13p = 106.27 - 90.45\n1.13p = 15.82\np = 15.82 / 1.13\np = 14\n#### 14", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: At a local gas station, Regular gasoline costs $2.96/gallon and Premium costs $4.10/gallon. A customer purchased a total of 10 gallons of both grades for $33.02. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 10\n2.96r + 4.10p = 33.02\nr = 10 - p\n2.96(10 - p) + 4.10p = 33.02\n29.60 - 2.96p + 4.10p = 33.02\n1.14p = 33.02 - 29.60\n1.14p = 3.42\np = 3.42 / 1.14\np = 3\n#### 3", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $2.93/gallon and Premium at $3.83/gallon. A customer buys a mixture of both grades totaling 14 gallons for a combined cost of $44.17. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 14\n2.93r + 3.83p = 44.17\nr = 14 - p\n2.93(14 - p) + 3.83p = 44.17\n41.02 - 2.93p + 3.83p = 44.17\n0.90p = 44.17 - 41.02\n0.90p = 3.15\np = 3.15 / 0.90\np = 7/2\n#### 7/2", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $3.12/gallon and Premium at $4.27/gallon. A customer buys a mixture of both grades totaling 15 gallons for a combined cost of $54.85. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 15\n3.12r + 4.27p = 54.85\nr = 15 - p\n3.12(15 - p) + 4.27p = 54.85\n46.80 - 3.12p + 4.27p = 54.85\n1.15p = 54.85 - 46.80\n1.15p = 8.05\np = 8.05 / 1.15\np = 7\n#### 7", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: At a local gas station, Regular gasoline costs $3.15/gallon and Premium costs $3.66/gallon. A customer purchased a total of 17 gallons of both grades for $54.06. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 17\n3.15r + 3.66p = 54.06\nr = 17 - p\n3.15(17 - p) + 3.66p = 54.06\n53.55 - 3.15p + 3.66p = 54.06\n0.51p = 54.06 - 53.55\n0.51p = 0.51\np = 0.51 / 0.51\np = 1\n#### 1", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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| 16 |
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{"prompt": "Question: At a local gas station, Regular gasoline costs $2.63/gallon and Premium costs $3.90/gallon. A customer purchased a total of 25 gallons of both grades for $94.96. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 25\n2.63r + 3.90p = 94.96\nr = 25 - p\n2.63(25 - p) + 3.90p = 94.96\n65.75 - 2.63p + 3.90p = 94.96\n1.27p = 94.96 - 65.75\n1.27p = 29.21\np = 29.21 / 1.27\np = 23\n#### 23", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $2.96/gallon and Premium at $4.45/gallon. A customer buys a mixture of both grades totaling 27 gallons for a combined cost of $115.68. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 27\n2.96r + 4.45p = 115.68\nr = 27 - p\n2.96(27 - p) + 4.45p = 115.68\n79.92 - 2.96p + 4.45p = 115.68\n1.49p = 115.68 - 79.92\n1.49p = 35.76\np = 35.76 / 1.49\np = 24\n#### 24", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: At a local gas station, Regular gasoline costs $3.11/gallon and Premium costs $4.70/gallon. A customer purchased a total of 16 gallons of both grades for $61.95. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 16\n3.11r + 4.70p = 61.95\nr = 16 - p\n3.11(16 - p) + 4.70p = 61.95\n49.76 - 3.11p + 4.70p = 61.95\n1.59p = 61.95 - 49.76\n1.59p = 12.19\np = 12.19 / 1.59\np = 23/3\n#### 23/3", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: At a local gas station, Regular gasoline costs $3.00/gallon and Premium costs $4.51/gallon. A customer purchased a total of 13 gallons of both grades for $54.10. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 13\n3.00r + 4.51p = 54.10\nr = 13 - p\n3.00(13 - p) + 4.51p = 54.10\n39.00 - 3.00p + 4.51p = 54.10\n1.51p = 54.10 - 39.00\n1.51p = 15.10\np = 15.10 / 1.51\np = 10\n#### 10", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: At a local gas station, Regular gasoline costs $2.54/gallon and Premium costs $3.89/gallon. A customer purchased a total of 16 gallons of both grades for $47.84. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 16\n2.54r + 3.89p = 47.84\nr = 16 - p\n2.54(16 - p) + 3.89p = 47.84\n40.64 - 2.54p + 3.89p = 47.84\n1.35p = 47.84 - 40.64\n1.35p = 7.20\np = 7.20 / 1.35\np = 16/3\n#### 16/3", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $2.64/gallon and Premium at $3.20/gallon. A customer buys a mixture of both grades totaling 24 gallons for a combined cost of $73.86. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 24\n2.64r + 3.20p = 73.86\nr = 24 - p\n2.64(24 - p) + 3.20p = 73.86\n63.36 - 2.64p + 3.20p = 73.86\n0.56p = 73.86 - 63.36\n0.56p = 10.50\np = 10.50 / 0.56\np = 75/4\n#### 75/4", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: At a local gas station, Regular gasoline costs $3.17/gallon and Premium costs $4.97/gallon. A customer purchased a total of 15 gallons of both grades for $59.43. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 15\n3.17r + 4.97p = 59.43\nr = 15 - p\n3.17(15 - p) + 4.97p = 59.43\n47.55 - 3.17p + 4.97p = 59.43\n1.80p = 59.43 - 47.55\n1.80p = 11.88\np = 11.88 / 1.80\np = 33/5\n#### 33/5", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: At a local gas station, Regular gasoline costs $2.66/gallon and Premium costs $4.21/gallon. A customer purchased a total of 29 gallons of both grades for $81.79. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 29\n2.66r + 4.21p = 81.79\nr = 29 - p\n2.66(29 - p) + 4.21p = 81.79\n77.14 - 2.66p + 4.21p = 81.79\n1.55p = 81.79 - 77.14\n1.55p = 4.65\np = 4.65 / 1.55\np = 3\n#### 3", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: At a local gas station, Regular gasoline costs $3.12/gallon and Premium costs $4.77/gallon. A customer purchased a total of 25 gallons of both grades for $101.10. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 25\n3.12r + 4.77p = 101.10\nr = 25 - p\n3.12(25 - p) + 4.77p = 101.10\n78.00 - 3.12p + 4.77p = 101.10\n1.65p = 101.10 - 78.00\n1.65p = 23.10\np = 23.10 / 1.65\np = 14\n#### 14", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $2.52/gallon and Premium at $4.25/gallon. A customer buys a mixture of both grades totaling 22 gallons for a combined cost of $84.85. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 22\n2.52r + 4.25p = 84.85\nr = 22 - p\n2.52(22 - p) + 4.25p = 84.85\n55.44 - 2.52p + 4.25p = 84.85\n1.73p = 84.85 - 55.44\n1.73p = 29.41\np = 29.41 / 1.73\np = 17\n#### 17", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $2.76/gallon and Premium at $3.40/gallon. A customer buys a mixture of both grades totaling 11 gallons for a combined cost of $34.20. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 11\n2.76r + 3.40p = 34.20\nr = 11 - p\n2.76(11 - p) + 3.40p = 34.20\n30.36 - 2.76p + 3.40p = 34.20\n0.64p = 34.20 - 30.36\n0.64p = 3.84\np = 3.84 / 0.64\np = 6\n#### 6", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $2.53/gallon and Premium at $4.24/gallon. A customer buys a mixture of both grades totaling 18 gallons for a combined cost of $60.93. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 18\n2.53r + 4.24p = 60.93\nr = 18 - p\n2.53(18 - p) + 4.24p = 60.93\n45.54 - 2.53p + 4.24p = 60.93\n1.71p = 60.93 - 45.54\n1.71p = 15.39\np = 15.39 / 1.71\np = 9\n#### 9", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $2.52/gallon and Premium at $3.31/gallon. A customer buys a mixture of both grades totaling 12 gallons for a combined cost of $36.56. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 12\n2.52r + 3.31p = 36.56\nr = 12 - p\n2.52(12 - p) + 3.31p = 36.56\n30.24 - 2.52p + 3.31p = 36.56\n0.79p = 36.56 - 30.24\n0.79p = 6.32\np = 6.32 / 0.79\np = 8\n#### 8", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: At a local gas station, Regular gasoline costs $3.09/gallon and Premium costs $4.59/gallon. A customer purchased a total of 30 gallons of both grades for $105.45. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 30\n3.09r + 4.59p = 105.45\nr = 30 - p\n3.09(30 - p) + 4.59p = 105.45\n92.70 - 3.09p + 4.59p = 105.45\n1.50p = 105.45 - 92.70\n1.50p = 12.75\np = 12.75 / 1.50\np = 17/2\n#### 17/2", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: At a local gas station, Regular gasoline costs $3.27/gallon and Premium costs $4.55/gallon. A customer purchased a total of 29 gallons of both grades for $101.87. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 29\n3.27r + 4.55p = 101.87\nr = 29 - p\n3.27(29 - p) + 4.55p = 101.87\n94.83 - 3.27p + 4.55p = 101.87\n1.28p = 101.87 - 94.83\n1.28p = 7.04\np = 7.04 / 1.28\np = 11/2\n#### 11/2", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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| 31 |
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $2.57/gallon and Premium at $4.15/gallon. A customer buys a mixture of both grades totaling 29 gallons for a combined cost of $107.71. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 29\n2.57r + 4.15p = 107.71\nr = 29 - p\n2.57(29 - p) + 4.15p = 107.71\n74.53 - 2.57p + 4.15p = 107.71\n1.58p = 107.71 - 74.53\n1.58p = 33.18\np = 33.18 / 1.58\np = 21\n#### 21", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: At a local gas station, Regular gasoline costs $3.39/gallon and Premium costs $5.35/gallon. A customer purchased a total of 27 gallons of both grades for $94.47. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 27\n3.39r + 5.35p = 94.47\nr = 27 - p\n3.39(27 - p) + 5.35p = 94.47\n91.53 - 3.39p + 5.35p = 94.47\n1.96p = 94.47 - 91.53\n1.96p = 2.94\np = 2.94 / 1.96\np = 3/2\n#### 3/2", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $2.99/gallon and Premium at $4.88/gallon. A customer buys a mixture of both grades totaling 23 gallons for a combined cost of $89.56. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 23\n2.99r + 4.88p = 89.56\nr = 23 - p\n2.99(23 - p) + 4.88p = 89.56\n68.77 - 2.99p + 4.88p = 89.56\n1.89p = 89.56 - 68.77\n1.89p = 20.79\np = 20.79 / 1.89\np = 11\n#### 11", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $3.32/gallon and Premium at $4.35/gallon. A customer buys a mixture of both grades totaling 18 gallons for a combined cost of $62.85. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 18\n3.32r + 4.35p = 62.85\nr = 18 - p\n3.32(18 - p) + 4.35p = 62.85\n59.76 - 3.32p + 4.35p = 62.85\n1.03p = 62.85 - 59.76\n1.03p = 3.09\np = 3.09 / 1.03\np = 3\n#### 3", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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| 35 |
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $2.54/gallon and Premium at $3.27/gallon. A customer buys a mixture of both grades totaling 12 gallons for a combined cost of $35.59. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 12\n2.54r + 3.27p = 35.59\nr = 12 - p\n2.54(12 - p) + 3.27p = 35.59\n30.48 - 2.54p + 3.27p = 35.59\n0.73p = 35.59 - 30.48\n0.73p = 5.11\np = 5.11 / 0.73\np = 7\n#### 7", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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| 36 |
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $3.47/gallon and Premium at $5.10/gallon. A customer buys a mixture of both grades totaling 14 gallons for a combined cost of $53.47. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 14\n3.47r + 5.10p = 53.47\nr = 14 - p\n3.47(14 - p) + 5.10p = 53.47\n48.58 - 3.47p + 5.10p = 53.47\n1.63p = 53.47 - 48.58\n1.63p = 4.89\np = 4.89 / 1.63\np = 3\n#### 3", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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| 37 |
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{"prompt": "Question: At a local gas station, Regular gasoline costs $3.03/gallon and Premium costs $3.75/gallon. A customer purchased a total of 12 gallons of both grades for $37.44. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 12\n3.03r + 3.75p = 37.44\nr = 12 - p\n3.03(12 - p) + 3.75p = 37.44\n36.36 - 3.03p + 3.75p = 37.44\n0.72p = 37.44 - 36.36\n0.72p = 1.08\np = 1.08 / 0.72\np = 3/2\n#### 3/2", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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| 38 |
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $2.60/gallon and Premium at $4.22/gallon. A customer buys a mixture of both grades totaling 25 gallons for a combined cost of $68.24. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 25\n2.60r + 4.22p = 68.24\nr = 25 - p\n2.60(25 - p) + 4.22p = 68.24\n65.00 - 2.60p + 4.22p = 68.24\n1.62p = 68.24 - 65.00\n1.62p = 3.24\np = 3.24 / 1.62\np = 2\n#### 2", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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| 39 |
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{"prompt": "Question: At a local gas station, Regular gasoline costs $2.64/gallon and Premium costs $3.32/gallon. A customer purchased a total of 18 gallons of both grades for $50.24. How many gallons of Premium were bought?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 18\n2.64r + 3.32p = 50.24\nr = 18 - p\n2.64(18 - p) + 3.32p = 50.24\n47.52 - 2.64p + 3.32p = 50.24\n0.68p = 50.24 - 47.52\n0.68p = 2.72\np = 2.72 / 0.68\np = 4\n#### 4", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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| 40 |
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{"prompt": "Question: A gas station sells two grades of gasoline: Regular at $3.36/gallon and Premium at $4.33/gallon. A customer buys a mixture of both grades totaling 16 gallons for a combined cost of $54.73. How many gallons of Premium gasoline did the customer purchase?\nAnswer:", "response": " Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\nr + p = 16\n3.36r + 4.33p = 54.73\nr = 16 - p\n3.36(16 - p) + 4.33p = 54.73\n53.76 - 3.36p + 4.33p = 54.73\n0.97p = 54.73 - 53.76\n0.97p = 0.97\np = 0.97 / 0.97\np = 1\n#### 1", "source": "tp_wordproblem", "tid": "032305a290", "level": "general"}
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{"tid": "032305a290", "cat": "wordproblem", "code": "import random\nfrom fractions import Fraction\n\ndef make(rng, original=False):\n if original:\n return (\n \"A gas station along Route 171 sells two grades of gasoline: Regular at $3.20/gallon and Premium at $4.10/gallon. A customer buys a mixture of both grades totaling 18 gallons for a combined cost of $63.60. How many gallons of Premium gasoline did the customer purchase?\",\n [\n \"Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\",\n \"r + p = 18\",\n \"3.20r + 4.10p = 63.60\",\n \"r = 18 - p\",\n \"3.20(18 - p) + 4.10p = 63.60\",\n \"57.60 - 3.20p + 4.10p = 63.60\",\n \"0.90p = 63.60 - 57.60\",\n \"0.90p = 6.00\",\n \"p = 6.00 / 0.90\",\n \"p = 20/3\"\n ],\n \"20/3\"\n )\n\n # Choose prices in cents to avoid float issues\n # Regular price between 250 and 350 cents, Premium between Regular+50 and Regular+200\n reg_cents = rng.randint(250, 350)\n prem_cents = reg_cents + rng.randint(50, 200)\n \n # Choose total gallons (integer) and premium gallons (rational)\n total_gal = rng.randint(10, 30)\n \n # We need to pick p such that total cost is a \"nice\" number (e.g., integer cents)\n # Let p = a/b. Cost = reg*(total - p) + prem*p = reg*total + (prem-reg)*p\n # Let diff = prem - reg. Cost = reg*total + diff*p.\n # We want Cost to be integer. So diff*p must be integer.\n # Let p = num / den. diff * num / den must be integer.\n # So den must divide diff * num.\n \n # Let's pick den from 1 to 10.\n den = rng.randint(2, 10) # Avoid 1 to make it a fraction usually, but 1 is okay if integer result\n # Actually, if den=1, p is integer. The original had a fraction. Let's allow both but ensure non-trivial.\n # To keep it similar to original (fractional answer), let's prefer den > 1.\n \n # Pick num such that 0 < num < total_gal * den (so p < total)\n # And p > 0\n # Also we want the final cost to be integer cents.\n # diff * num / den = integer => num * diff is divisible by den.\n \n valid_p = []\n for num in range(1, total_gal * den):\n if (num * (prem_cents - reg_cents)) % den == 0:\n p = Fraction(num, den)\n if 0 < p < total_gal:\n # Check if r = total - p is also positive (already true)\n # Check if the cost is a \"reasonable\" money amount (e.g., not too huge, but it's fine)\n valid_p.append(p)\n \n if not valid_p:\n return None\n\n p = rng.choice(valid_p)\n r = total_gal - p\n \n # Calculate total cost in cents\n total_cost_cents = reg_cents * r + prem_cents * p\n # total_cost_cents should be an integer because of the condition above\n if total_cost_cents.denominator != 1:\n return None\n total_cost_cents = int(total_cost_cents)\n \n # Format prices and cost\n reg_price = f\"{reg_cents // 100}.{reg_cents % 100:02d}\"\n prem_price = f\"{prem_cents // 100}.{prem_cents % 100:02d}\"\n total_cost = f\"{total_cost_cents // 100}.{total_cost_cents % 100:02d}\"\n \n # Ensure the problem is not trivial (e.g., p is not 0 or total)\n if p == 0 or p == total_gal:\n return None\n \n # Vary wording slightly\n templates = [\n \"A gas station sells two grades of gasoline: Regular at ${rp}/gallon and Premium at ${pp}/gallon. A customer buys a mixture of both grades totaling {tg} gallons for a combined cost of ${tc}. How many gallons of Premium gasoline did the customer purchase?\",\n \"At a local gas station, Regular gasoline costs ${rp}/gallon and Premium costs ${pp}/gallon. A customer purchased a total of {tg} gallons of both grades for ${tc}. How many gallons of Premium were bought?\",\n ]\n question = rng.choice(templates).format(rp=reg_price, pp=prem_price, tg=total_gal, tc=total_cost)\n \n # Build solution lines\n # r + p = total\n # reg*r + prem*p = cost\n # r = total - p\n # reg*(total - p) + prem*p = cost\n # reg*total - reg*p + prem*p = cost\n # (prem - reg)*p = cost - reg*total\n # p = (cost - reg*total) / (prem - reg)\n \n diff_cents = prem_cents - reg_cents\n reg_total_cost_cents = reg_cents * total_gal\n rhs_cents = total_cost_cents - reg_total_cost_cents\n \n # Format numbers for lines\n # Use fractions for exact representation in lines if needed, but original used decimals.\n # Original: \"0.90p = 6.00\". \n # Let's stick to decimal formatting for the lines to match the style, but ensure exactness.\n \n # Helper to format cents to string\n def fmt_cents(c):\n return f\"{c // 100}.{c % 100:02d}\"\n \n lines = [\n f\"Let r be the gallons of Regular gasoline and p be the gallons of Premium gasoline.\",\n f\"r + p = {total_gal}\",\n f\"{reg_price}r + {prem_price}p = {total_cost}\",\n f\"r = {total_gal} - p\",\n f\"{reg_price}({total_gal} - p) + {prem_price}p = {total_cost}\",\n ]\n \n # Calculate intermediate values for the line\n # reg * total\n reg_total_str = fmt_cents(reg_total_cost_cents)\n # diff\n diff_str = fmt_cents(diff_cents)\n # rhs\n rhs_str = fmt_cents(rhs_cents)\n \n lines.append(f\"{reg_total_str} - {reg_price}p + {prem_price}p = {total_cost}\")\n lines.append(f\"{diff_str}p = {total_cost} - {reg_total_str}\")\n lines.append(f\"{diff_str}p = {rhs_str}\")\n lines.append(f\"p = {rhs_str} / {diff_str}\")\n \n # Final answer format\n # If p is an integer, format as int. Else as fraction.\n if p.denominator == 1:\n ans_str = str(p.numerator)\n else:\n ans_str = f\"{p.numerator}/{p.denominator}\"\n \n lines.append(f\"p = {ans_str}\")\n \n return (question, lines, ans_str)\n"}
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