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abdulhakeem 2025-01-30 23:44:12 -06:00
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{
"question": "A man eats 5 sandwiches per day, his wife eats 4 sandwiches per day, and their son eats 2 sandwiches per day. How many sandwiches does this family eat in one week?",
"answer": "The number of sandwiches they eat in one day is 5 + 4 + 2 = <<5+4+2=11>>11 sandwiches.\nThe number of sandwiches they eat in a week is 11 * 7 = <<11*7=77>>77 sandwiches.\n#### 77",
"id_orig": 1023,
"id_shuffled": 26,
"question_annotated": "{name1,A man} eats {n1,5} {food,sandwiches} per day, {name2,his wife} eats {n2,4} {food,sandwiches} per day, and their {relation,son} eats {frac,quarter} of the combined number of {food,sandwiches} they eat per day. After one month, the family decides to go on a diet in the second month, reducing their food consumption by {p1,20}% for the first half of the month, and then by an additional {p2,15}% for the second half. How many {food,sandwiches} does this family eat in two months?\n\n#init:\n- name1 = sample([\"A father\", \"A grandfather\", \"An uncle\"])\n- name2 = sample([\"his wife\", \"his partner\", \"his spouse\"])\n- relation = sample([\"daughter\", \"son\", \"grandchild\"])\n- food = sample([\"pizzas\", \"burritos\", \"tacos\", \"sushi rolls\", \"hamburgers\"])\n- $frac = sample(fraction_alph)\n- $n1 = range(4, 26)\n- $n2 = range(4, 26)\n- $p1= list([4, 5, 10, 15, 20, 25, 30, 40, 50, 60, 75, 80, 90])\n- $p2 = list([4, 5, 10, 15, 20, 25, 30, 40, 50, 60, 75, 80, 90])\n\n#conditions:\n- (n1 + n2) * frac > 2\n- is_int((n1 + n2) * frac)\n- is_int(n1 * p1 / 100)\n- is_int(n2 * p1 / 100)\n- is_int(((n1 + n2) * (frac)) * p1 / 100)\n- is_int(n1 * (100-p1) / 100 * p2 / 100)\n- is_int(n2 * (100-p1) / 100 * p2 / 100)\n- is_int(((n1 + n2) * (frac) ) * (100-p1) / 100 * p2 / 100)\n- is_int(((n1 + n2) * (frac+1) ) * (100-p1) / 100 * p2 / 100)\n\n#answer: int(((n1 + n2) * (1+frac) ) * 30 + ((n1 + n2) * (1+frac)) * 15 * (100-p1) / 100 + ((n1 + n2) * (1+frac) - 1) * 15 * (100-p1) / 100 * (100 - p2) / 100)",
"answer_annotated": "{name1} and {name2} consumption: {n1} + {n2} = {n1 + n2}\n{relation} consumes {frac} more than {name1} and {name2} combined: {n1+n2} * {frac} = {int(frac * (n1+n2))}. So {relation} consumes {n1+n2} + {int(frac * (n1+n2))} = {int(((n1 + n2) * (1+frac)))} {food}.\nDuring first month they consume 30 * {int(((n1 + n2) * (1+frac)))} = {30 * int(((n1 + n2) * (1+frac)))}.\nThe first half of the second month the consume {p1}% less each day: {100-p1}% * {int(((n1 + n2) * (1+frac)))} = {int(((n1 + n2) * (1+frac) * (100-p1)/100))} . So in 15 days, they consume {int(((n1 + n2) * (1+frac)) * 15 * (100-p1) / 100)} {food}. \nDuring second month, they consume {p2}% less than the first half each day, so they consume {100-p2}% * {int(((n1 + n2) * (1+frac) * (100-p1)/100))} = {int(((n1 + n2) * (1+frac) * (100-p1)/100 * (100-p2)/100))}. So in 15 days, they consume 15 * {int(((n1 + n2) * (1+frac) * (100-p1)/100 * (100-p2)/100))} = {int(((n1 + n2) * (1+frac) * (100-p1)/100 * (100-p2)/100)) * 15} {food}.\nIn 2 months, they consume {int(((n1 + n2) * (1+frac)))} + {int(((n1 + n2) * (1+frac)) * 15 * (100-p1) / 100)} + {int(((n1 + n2) * (1+frac) * (100-p1)/100 * (100-p2)/100)) * 15} = { int(((n1 + n2) * (1+frac)) * 30 + ((n1 + n2) * (1+frac)) * 15 * (100-p1) / 100 + ((n1 + n2) * (1+frac)) * 15 * (100-p1) / 100 * (100 - p2) / 100)} {food} together.\n#### { int(((n1 + n2) * (1+frac)) * 30 + ((n1 + n2) * (1+frac)) * 15 * (100-p1) / 100 + ((n1 + n2) * (1+frac)) * 15 * (100-p1) / 100 * (100 - p2) / 100)}"
}