AMC 8 2010 Problem 21
AMC8 2010 年第 21 题
方程与不等式★★★☆☆
Hui is an avid reader. She bought a copy of the best seller Math is Beautiful. On the first day, Hui read 1/5 of the pages plus 12 more, and on the second day she read 1/4 of the remaining pages plus 15 pages. On the third day she read 1/3 of the remaining pages plus 18 pages. She then realized that there were only 62 pages left to read, which she read the next day. How many pages are in this book?
Hui 很爱读她买的一本名叫《数学是美丽的》的畅销书，第一天，Hui 读了书的 1/5 再加 12 页，第二天，她读了剩下的 1/4 再加 15 页。第三天，她读了剩余页数的 1/3 再加 18 页。然后她发现还剩 62 页未读，隔天就把这剩下的 62 页读完了。问这本书总共多少页？
- A.120
- B.180
- C.240
- D.300
- E.360
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
Reason backward as follows. On the third day, Hui reads 1 3 3 1 of the remaining pages plus 18 18 more, leaving her with 62 62 pages left to read. This means that 62 + 18 = 80 62+18=80 is 2 3 3 2 of the number of pages remaining at the end of the second day. She had 3 2 × 80 = 120 2 3 ×80=120 pages left to read at the end of the second day. On the second day she read 1 4 4 1 of the remaining pages plus 15 15 more, so 120 + 15 = 135 120+15=135 is 3 4 4 3 of the number of pages remaining at the end of the first day. She had 4 3 × 135 = 180 3 4 ×135=180 pages left to read at the end of the first day. On the first day she read 1 5 5 1 of the pages plus 12 12 more. So 180 + 12 = 192 180+12=192 is 4 5 5 4 of the number of pages in the book. The total number of pages is 5 4 × 192 = 240 4 5 ×192=240. OR OR Setup a chart working backwards through the days, to show the number of pages that Hui has left to read each day. Day Extra Pages Read Fraction Read Fraction Left Calculation Pages to be Read 4 0 62 3 18 1 3 2 3 62 + 18 2 / 3 120 2 15 1 4 3 4 120 + 15 3 / 4 180 1 12 1 5 4 5 180 + 12 4 / 5 240 Day 4 3 2 1 Extra Pages Read 0 18 15 12 Fraction Read 3 1 4 1 5 1 Fraction Left 3 2 4 3 5 4 Calculation 2/3 62+18 3/4 120+15 4/5 180+12 Pages to be Read 62 120 180 240 Answer: 𝐶 C .
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