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8 lines
No EOL
2 KiB
JSON
8 lines
No EOL
2 KiB
JSON
{
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"question": "Benny saw a 10-foot shark with 2 6-inch remoras attached to it. What percentage of the shark's body length is the combined length of the remoras?",
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"answer": "First, find the combined length of the remoras in inches: 6 inches/remora * 2 remoras = <<6*2=12>>12 inches\nThen divide that number by 12 to convert it to feet: 12 inches / 12 inches/foot = <<1=1>>1 foot\nThen divide the combined remora length in feet by the shark's length and multiply by 100% to express the answer as a percentage: 1 foot / 10 feet * 100% = 10%\n#### 10",
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"id_orig": 473,
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"id_shuffled": 0,
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"question_annotated": "{n, Benny} saw a {x,10}-foot {big_fish,shark} with {k,2} {y,6}-inch remoras attached to it. But {frac,half} of the remoras go away. What percentage of the {big_fish,shark}'s body length is the combined length of the remaining remoras?\n\n#init:\n- n = sample(names)\n- big_fish = sample([\"dolphin\", \"whale\", \"shark\"])\n- $x = range(30, 90)\n- $k = range(12, 55)\n- $y = range(9, 37, 3)\n- $frac = sample(fractions)\n\n#conditions:\n- k * y < x * 12\n- is_int(frac * k)\n- frac* k > 2\n- divides(x * 12, (k-frac*k)*y)\n- divides(100, x * 12 / ((k-frac*k)*y))\n- int(((k-k*frac) * y)/ (x * 12) * 100) != 25 and int(((k-k*frac) * y)/ (x * 12) * 100) != 50\n\n#answer: int(((k-k*frac) * y)/ (x * 12) * 100)",
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"answer_annotated": "First, find the total number of remoras remaining: {k} - {k}*{frac} = <<{k}-{k}*{frac}>> {int(k*(1-frac))}.\nThen, find the combined length of the remoras in inches: {y} inches/remora * {int(k*(1-frac))} remoras = <<{y}*{int(k*(1-frac))}={int(k*(1-frac))*y}>>{int(k*(1-frac))*y} inches.\nThen divide that number by 12 to convert it to feet: {k*y} inches / 12 inches/foot = <<{int(k*(1-frac))*y}/12>>{int(k*(1-frac))*y//12} foot.\nThen divide the combined remora length in feet by the {big_fish}'s length and multiply by 100% to express the answer as a percentage: {int(k*(1-frac))*y//12} foot / {x} feet * 100% = {int(int(k*(1-frac))*y/(12*x)*100)}%\n\n#### {int(k*(1-frac)*y/(12*x)*100)}"
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} |