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abdulhakeem 2025-01-30 23:44:12 -06:00
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{
"question": "Martha is knitting winter wear for her 3 grandchildren. They're triplets, so they're all the same size. She wants to make a hat, scarf, sweater, mittens, and socks for each of them. It takes 2 skeins of wool to make a hat, 4 for a scarf, 12 for a sweater, 1 for a pair of mittens, and 2 for a pair of socks. How many skeins of wool will she need to buy?",
"answer": "A full outfit for each child will require 2 skeins per hat + 4 skeins per scarf + 12 skeins per sweater + 1 skein per pair of mittens + 2 skeins per pair of socks = <<2+4+12+1+2=21>>21 skeins of wool.\nSo to knit outfits for all of her grandchildren, she will need 3 * 21 = <<3*21=63>>63 skeins of wool.\n#### 63",
"id_orig": 520,
"id_shuffled": 23,
"question_annotated": "{name,Martha} is knitting winter wear for her {count,3} grandchildren. They're {children,triplets}, so they're all the same size. She wants to make a {c1,hat}, {c2,scarf}, {c3,sweater}, {c4,mittens}, and {c5,socks} for each of them. It takes {n1,2} skeins of wool to make a {c1,hat}, {n2,4} for a {c2,scarf}, {n3,12} for a {c3,sweater}, {n4,1} for a pair of {c4,mittens}, and {n5,2} for a pair of {c5,socks}. {name, Martha} wants to make two warm jackets for herself, each needing {extra,10} skeins of wool. Each dozen skeins of wool costs ${price,7}. The store has a promotion where customers receive a $20 discount on purchases over ${limit,200}. How much should {name,Martha} pay for all the skeins of wool she needs?\n\n#init:\n- name = sample(names_female)\n- c1, c2, c3 = sample([\"sweater\", \"shawl\", \"hat\", \"cardigan\", \"poncho\", \"vest\", \"beanie\", \"tunic\"],3)\n- c4, c5 = sample([ \"mittens\", \"booties\", \"socks\", \"leg warmers\", \"gloves\"], 2)\n- $n1 = range(3, 7)\n- $n2 = range(3, 7)\n- $n3 = range(8, 13)\n- $n4 = range(8, 13)\n- $n5 = range(9, 16)\n- $count = list(range(2, 6))\n- $extra = range(3, 13)\n- $children = sample([(\"twins\",2), (\"triplets\",3), (\"quadruplets\", 4), (\"quintuplets\", 5)]* 10)\n- $price = range(6, 10)\n- $limit = range(100, 301, 100)\n\n#conditions:\n- divides(count*(n1+n2+n3+n4+n5) + 2*extra, 12)\n- count == children\n- limit < (count*(n1+n2+n3+n4+n5) + 2*extra)//12*price < limit + 200\n\n#answer: ((count*(n1+n2+n3+n4+n5) + 2*extra) // 12 * price) - 20",
"answer_annotated": "A full outfit for each child will require {n1} skeins per {c1} + {n2} skeins per {c2} + {n3} skeins per {c3} + {n4} skeins per pair of {c4} + {n5} skeins per pair of {c5} = <<{n1}+{n2}+{n3}+{n4}+{n5}={n1+n2+n3+n4+n5}>>{n1+n2+n3+n4+n5} skeins of wool.\nSo to knit outfits for all of her grandchildren, she will need {count}*{n1+n2+n3+n4+n5} = <<{count}*{n1+n2+n3+n4+n5}={count*(n1+n2+n3+n4+n5)}>>{count*(n1+n2+n3+n4+n5)} skeins of wool.\nWe add the {extra} skeins for the jacket. 2*{extra} + {count*(n1+n2+n3+n4+n5)} = {count*(n1+n2+n3+n4+n5)+2*extra}.\n{name} needs {count*(n1+n2+n3+n4+n5)+2*extra} skeins so that would be {count*(n1+n2+n3+n4+n5)+2*extra} / 12 = {(count*(n1+n2+n3+n4+n5)+2*extra) // 12} dozen. The cost is {(count*(n1+n2+n3+n4+n5)+2*extra) // 12} * {price} = {(count*(n1+n2+n3+n4+n5)+2*extra) // 12 * price}. Since {(count*(n1+n2+n3+n4+n5)+2*extra) // 12 * price} is more that {limit}, {name} receives $20 discount. So her total bill is {(count*(n1+n2+n3+n4+n5)+2*extra) // 12 * price} - 20 = {((count*(n1+n2+n3+n4+n5)+2*extra) // 12 * price) - 20} \n#### {((count*(n1+n2+n3+n4+n5)+2*extra) // 12 * price) - 20}"
}