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8 lines
No EOL
3.7 KiB
JSON
8 lines
No EOL
3.7 KiB
JSON
{
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"question": "Frankie watches TV after he finishes his homework every night. On Monday and Tuesday, he watched a 1-hour episode of his favorite show each night. On Wednesday, he watched a few episodes of a 30-minute show. On Thursday, he finished homework early and watched a 1-hour episode and a 30-minute show. On Friday, he got to stay up late for the weekend, so he watched two 1-hour episodes. If he watched 7 hours of TV in all, how many 30-minute episodes did he watch on Wednesday?",
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"answer": "Let W be the number of episodes he watched on Wednesday.\nAfter Monday, he had 7 - 1 = <<7-1=6>>6 hours of TV left.\nAfter Tuesday, he had 6 - 1 = <<6-1=5>>5 hours of TV left.\nAfter Thursday, he had 5 - 1 - 1/2 = 3 1/2 hours of TV left.\nAfter Friday, he had 3 1/2 - 2 = 1 1/2 hours of TV left.\nEach 30-minute episode is 1/2 hour.\nThus, W = 1 1/2 / 1/2 = 3 episodes.\n#### 3",
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"id_orig": 107,
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"id_shuffled": 21,
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"question_annotated": "{name,Frankie} watches TV after he finishes his homework every night. On {d1,Monday} and {d2,Tuesday}, he watched {h1,1}-hour episodes of his favorite show each night. On {d3,Wednesday}, he watched a few episodes of a {m1,30}-minute show. On {d4,Thursday}, he finished homework early and watched a {h2,1}-hour episode and a {m2,30}-minute show. On {d5,Friday}, he got to stay up late, so he watched {n2,two} {h3,1}-hour episodes. On {d6, Saturday}, he watched {extra,three} episodes, each {extra_mins,45} minutes. If he watched {total,7} hours of TV in all, how many {m1,30}-minute episodes did he watch on {d3,Wednesday}?\n\n#init:\n- name = sample(names_male)\n- d1, d2, d3, d4, d5, d6 = sample_sequential(weekdays, 6)\n- $total = range(18, 33)\n- $h1 = range(3, 7)\n- $h3 = range(2, 6)\n- $m1 = range(15, 61, 15)\n- $m2 = range(15, 61, 15)\n- $h2 = range(2, 7)\n- $n2 = numbers_within(2, 5)\n- $ans = range(1, 8)\n- $extra = numbers_within(2, 5)\n- $extra_mins = range(15, 46, 15)\n\n#conditions: \n- divides(m1, 15)\n- divides(m2, 15)\n- total * 60 == 2* h1 * 60 + ans * m1 + h2 * 60 + m2 + n2* h3 * 60 + extra_mins * extra\n\n#answer: $ans",
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"answer_annotated": "Let {d3[0]} be the minutes of TV {name} had watched on {d3}.\nAfter {d1}, he had watched {h1} hours = {h1} * 60 = {h1*60} minutes of TV.\nOn {d2}, he watched {h1} * 60 = {h1*60} minutes of TV, so in total he watched {h1*2*60} minutes on {d1} and {d2}.\nOn {d4}, he watched {h2}*60 + {m2} = {h2 * 60} + {m2} minutes of TV. So, in total, he watched {h1*120} + {h2*60} + {m2} = {h1*120 + h2*60 + m2} minutes on {d1}, {d2}, and {d4} combined.\nOn {d5}, he watched {n2} episodes, each {h3} * 60 = {h3*60} minutes, which would be {n2} * {h3*60} = {n2 * h3 * 60} minutes. So far he watched {h1*120 + h2*60 + m2} + {n2*h3*60} = {h1*120 + h2*60 + m2 + n2*h3*60} minutes on {d1}, {d2}, {d4}, and {d5} combined. \nFinally, on {d6}, he watched {extra} * {extra_mins} = {extra * extra_mins} minutes of TV.\nSo, overall, {name} has watched {h1*120 + h2*60 + m2 + n2*h3*60} + {extra*extra_mins} = {h1*120 + h2*60 + m2 + n2*h3*60 + extra*extra_mins} minutes of TV on {d1}, {d2}, {d4}, {d5}, {d6}.\nWe know that overall, {name} had watched {total} hours of TV, which would be {total} * 60 = {total * 60} minutes. So we know {h1*120 + h2*60 + m2 + n2*h3*60 + extra*extra_mins} + {d3[0]} = {total*60}. Hence, {d3[0]} = {total*60} - {h1*120 + h2*60 + m2 + n2*h3*60 + extra*extra_mins} = {total*60 - (h1*120 + h2*60 + m2 + n2*h3*60 + extra*extra_mins)}. \nTo calculate the number of episodes on {d3}, we divide the total amount of TV watched on {d3} by the episode length: {total*60 - (h1*120 + h2*60 + m2 + n2*h3*60 + extra*extra_mins)} minutes / {m1} minutes per episode = {(total*60 - (h1*120 + h2*60 + m2 + n2*h3*60 + extra*extra_mins))//m1} episodes.\n\n#### {ans}"
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} |