mirror of
https://github.com/open-thought/reasoning-gym.git
synced 2026-04-28 17:29:39 +00:00
8 lines
No EOL
1.8 KiB
JSON
8 lines
No EOL
1.8 KiB
JSON
{
|
|
"question": "If Sam and Harry have 100 feet of fence between them, and they agree to split it with Harry getting 60 feet more than Sam, how much is left over for Sam?",
|
|
"answer": "Let x be the amount of fence Sam gets and y be the amount Harry gets. We know that y = x + 60, and y + x = 100.\nSubstituting the first equation into the second equation, we get 2x+60=100\nSubtracting the 60 from both sides, we get 2x=40\nWe divide each side by two, leaving x=20. This means Sam has 20 feet of fence left over.\n#### 20",
|
|
"id_orig": 1084,
|
|
"id_shuffled": 85,
|
|
"question_annotated": "{name1,Sam}, {name2,Harry}, and {name3,Sara} have {total,100} {unit,feet} of fence between them. They agree to split it with {name2,Harry} getting {diff,60} {unit,feet} more than {name1,Sam}, and {name3,Sara} getting {diff2,10} {unit,feet} more than {name2,Harry}. How much is left over for {name1,Sam}?\n\n#init:\n- name1, name2, name3 = sample(names, 3)\n- unit = sample([\"feet\", \"yards\", \"meters\"])\n- $total = range(100, 1000, 20)\n- $diff = range(10, 200, 10)\n- $diff2 = range(10, 200, 10)\n\n#conditions:\n- total - 2*diff - diff2 > 10\n- divides((total - 2*diff-diff2) , 3)\n\n#answer: (total - 2*diff-diff2) // 3",
|
|
"answer_annotated": "Let x be the amount of fence {name1} gets, y be the amount {name2} gets, and z be the amount {name3} gets. We know that y = x + {diff}, z = y + {diff2} = x + {diff+diff2}, and y + x + z = {total}.\nSubstituting the first equation into the final equation, we get {total} = (x + {diff}) + x + (x+{diff+diff2}). So we have {total} = 3*x + {2*diff+diff2}.\nSubtracting the {2*diff+diff2} from both sides, we get 3x={total-2*diff-diff2}\nWe divide each side by three, leaving x={(total-2*diff-diff2)//3}. This means {name1} gets {(total-2*diff-diff2)//3} {unit} of fence.\n#### {(total-2*diff-diff2)//3}"
|
|
} |