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abdulhakeem 2025-01-30 23:44:12 -06:00
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{
"question": "James gets 80 emails a day. 20% of those emails don't require any response. He responds to the rest of them. How many emails does he respond to in a 5 day work week?",
"answer": "He gets 80*.2=<<80*.2=16>>16 emails he doesn't need to respond to\nSo he responds to 80-16=<<80-16=64>>64 emails\nSo he responds to 64*5=<<64*5=320>>320 emails a week\n#### 320",
"id_orig": 1063,
"id_shuffled": 27,
"question_annotated": "{name,James} receives {n,80} emails a day. {p,20}% of those emails don't require any response. From the rest, {name,James} can only respond to {k,5} less than the {frac,half} of them. How many emails does {name,James} respond to in a {d,5} day work week? {name,James} work overtime on the last day so he can respond to {pp,10}% more emails than usual.\n\n#init:\n- name = sample(names_male)\n- $n = range(10, 35)\n- $p = range(5, 40)\n- $k = range(2, 21)\n- $frac = sample(fractions)\n- $d = range(3, 7)\n- $pp = range(5, 76, 5)\n\n#conditions:\n- is_int(n * p / 100)\n- is_int(n * (100 - p) / 100)\n- (n * (100 - p) / 100) * (frac) > k + 7\n- is_int((n * (100 - p) / 100) * (frac))\n- is_int((1+pp/100)*(((n * (100 - p) / 100) * frac)-k))\n\n#answer: int((d-1) * (((n * (100 - p) / 100) * frac)-k)) + int((1+pp/100)*(((n * (100 - p) / 100) * frac)-k))",
"answer_annotated": "{name} receives {int(n * p / 100)}=<<{n}*{p}/100={n*p//100}>>{n*p//100} emails that don't require a response\nSo {n}-{n*p//100}=<<{n}-{n*p//100}={n*(100-p)//100}>>{n*(100-p)//100} emails will be left. Of those, {name} can respond to {frac} minus {k}. So {n*(100-p)//100} * {frac} - {k} = {int((n*(100-p)//100)*frac)-k} emails will be responded in a day.\nIn the first {d-1} day work week, {name} responds to {int((n*(100-p)//100)*frac)-k}*{d-1}=<<{int((n*(100-p)//100)*frac)-k}*{d-1}={(d-1)*(int((n*(100-p)//100)*frac)-k)}>> {(d-1)*(int((n*(100-p)//100)*frac)-k)} emails. \nIn the last day, {name} responds to {pp}% more email so {pp}% * {int((n*(100-p)//100)*frac)-k} = {int((pp/100)*(int((n*(100-p)//100)*frac)-k))} emails. So on that day, he responds to {int(pp/100*(int((n*(100-p)//100)*frac)-k))} + {int((n*(100-p)//100)*frac)-k} = {int((1+pp/100)*(int((n*(100-p)//100)*frac)-k))} emails.\nOverall, in {d} days, {name} responds to {(d-1)*(int((n*(100-p)//100)*frac)-k)} emails +{int((1+pp/100)*(int((n*(100-p)//100)*frac)-k))} emails = {int((d-1) * (((n * (100 - p) / 100) * frac)-k)) + int((1+pp/100)*(((n * (100 - p) / 100) * frac)-k))} emails.\n#### {int((d-1) * (((n * (100 - p) / 100) * frac)-k)) + int((1+pp/100)*(((n * (100 - p) / 100) * frac)-k))}"
}