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abdulhakeem 2025-01-30 23:44:12 -06:00
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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?",
"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",
"id_orig": 473,
"id_shuffled": 0,
"question_annotated": "{n, Benny} saw a {x,10}-foot {big_fish,shark} with {k,2} remoras, each {y,6} inches long attached to it. Then, {frac,half} of the remoras swam away. Later, {n, Benny} saw another {x2,15}-foot {big_fish,shark} with {k2,3} remoras, each {y2,3} inches long, attached to it. On average, what percentage of each {big_fish,shark}'s body length is covered by the remoras?\n\n\n#init:\n- n = sample(names)\n- big_fish = sample([\"dolphin\", \"whale\", \"shark\"])\n- $x = range(30, 50)\n- $k = range(12, 25)\n- $y = range(12, 25)\n- $k2 = range(4, 9)\n- $y2 = range(3, 9)\n- $x2 = range(8, 13)\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- is_int(k2*y2/(x2*12)*100)\n\n#answer: (int(((k-k*frac) * y)/ (x * 12) * 100) + int(k2*y2/(x2*12)*100))/2",
"answer_annotated": "First {big_fish}:\nFirst, 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: {int(k*(1-frac))*y} inches / 12 inches/foot = <<{int(k*(1-frac))*y}/12>>{int(k*(1-frac))*y//12} feet.\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} feet / {x} feet * 100% = {int(int(k*(1-frac))*y/(12*x)*100)}%\nSecond {big_fish}:\nThe length of the second {big_fish} is {x2}*12 = {x2*12} inches\nThe lengths of remoras: {k2} * {y2} = {k2*y2} inches.\nThe percentage is {k2*y2} inches / {x2*12}inches = {k2*y2 / (x2*12)} = {int(k2*y2 / (x2 *12)* 100)}%.\nThe average percentage is:\n({int(int(k*(1-frac))*y/(12*x)*100)}% + {int(k2*y2 / (x2*12) * 100)}%) / 2 = {(int(((k-k*frac) * y)/ (x * 12) * 100) + int(k2*y2/(x2*12)*100))/2}%\n#### {(int(((k-k*frac) * y)/ (x * 12) * 100) + int(k2*y2/(x2*12)*100))/2}"
}