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8 lines
No EOL
3 KiB
JSON
8 lines
No EOL
3 KiB
JSON
{
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"question": "There are 6 periods in the day for a normal student but John has to take 2 extra classes. Each class is 40 minutes long. He goes to class for 5 days a week. He then spends 1/16 of his weekly minutes each on Saturday and Sunday as extra learning time. How many hours a week does he spend learning?",
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"answer": "He takes 6+2=<<6+2=8>>8 classes a day\nThat means he spends 40*8=<<40*8=320>>320 minutes per day in class\nSo he spends 320*5=<<320*5=1600>>1600 minutes a week\nThat means he spends 1600/16=<<1600/16=100>>100 minutes each on Saturday and Sunday\nSo he spends 1600+100+100=<<1600+100+100=1800>>1800 minutes per week\nSo he spends 1800/60=<<1800/60=30>>30 hours per week\n#### 30",
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"id_orig": 1088,
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"id_shuffled": 78,
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"question_annotated": "There are {n1,6} periods in the day for a normal student but {name,John} has to take {n2,2} extra classes. Each class is {t,40} minutes long, but he spends {tt,10} minutes before each class to review the study materials and prepare. He goes to class for {d,5} days a week. He then spends {frac,1/16} of his weekly minutes each on Saturday and Sunday as extra learning time. How many hours a week does he spend learning?\n\n#init:\n- name = sample(names_male)\n- $n1 = range(5, 10)\n- $n2 = range(2, 6)\n- $t = range(30, 61, 5)\n- $tt = range(5, 16, 5)\n- $d = range(4, 6)\n- $frac = sample(fraction_alnum)\n\n#conditions:\n- (n1 + n2) * (t+tt) < 721\n- is_int((n1 + n2) * (t+tt) * d * frac)\n- (n1 + n2) * (t+tt) * d * frac < 250\n- is_int(((n1 + n2) * (t+tt) * d + 2 * (n1 + n2) * (t+tt) * d * frac) / 60)\n\n#answer: ((n1 + n2) * (t+tt) * d + 2 * (n1 + n2) * (t+tt) * d * frac) // 60",
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"answer_annotated": "He takes {n1}+{n2}=<<{n1}+{n2}={n1+n2}>>{n1+n2} classes a day\nThat means he spends {t}*{n1+n2}=<<{t}*{n1+n2}={t*(n1+n2)}>>{t*(n1+n2)} minutes per day in class. He also spends {tt} minutes before each class to prepare, so that would be {tt}*{n1+n2}=<<{tt}*{n1+n2}={tt*(n1+n2)}>>{tt*(n1+n2)} minutes. Overall, he spends {t*(n1+n2)} + {tt*(n1+n2)} = {(t+tt)*(n1+n2)} minutes for classes each day.\nSo he spends {(t+tt)*(n1+n2)}*{d}=<<{(t+tt)*(n1+n2)}*{d}={(t+tt)*(n1+n2)*d}>>{(t+tt)*(n1+n2)*d} minutes a week for classes.\nThat means he spends {(t+tt)*(n1+n2)*d}*{frac}=<<{(t+tt)*(n1+n2)*d}*{frac}={int((n1 + n2) * (t+tt) * d * frac)}>>{int((n1 + n2) * (t+tt) * d * frac)} minutes each on Saturday and Sunday.\nSo he spends {(t+tt)*(n1+n2)*d}+{int((n1 + n2) * (t+tt) * d * frac)}+{int((n1 + n2) * (t+tt) * d * frac)}=<<{(t+tt)*(n1+n2)*d}+{int((n1 + n2) * (t+tt) * d * frac)}+{int((n1 + n2) * (t+tt) * d * frac)}={(t+tt)*(n1+n2)*d + 2*int((n1 + n2) * (t+tt) * d * frac)}>>{(t+tt)*(n1+n2)*d + 2*int((n1 + n2) * (t+tt) * d * frac)} minutes per week.\nSo he spends {(t+tt)*(n1+n2)*d + 2*int((n1 + n2) * (t+tt) * d * frac)}/60=<<{(t+tt)*(n1+n2)*d + 2*int((n1 + n2) * (t+tt) * d * frac)}/60={((n1 + n2) * (t+tt) * d + 2 * (n1 + n2) * (t+tt) * d * frac) // 60}>>{((n1 + n2) * (t+tt) * d + 2 * (n1 + n2) * (t+tt) * d * frac) // 60} hours per week\n#### {((n1 + n2) * (t+tt) * d + 2 * (n1 + n2) * (t+tt) * d * frac) // 60}"
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} |