2010 AMC 8 第 21 题
先试着解答 2010 AMC 8 第 21 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2010 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
21.
惠很爱读书。她买了一本畅销书《数学真美》。第一天，惠读了全书页数的 又多读 页；第二天，她读了剩余页数的 又多读 页；第三天，她读了剩余页数的 又多读 页。随后她发现只剩 页要读，并在次日读完。这本书共有多少页？
Hui is an avid reader. She bought a copy of the bestseller Math is Beautiful. On the first day, Hui read of the pages plus more, and on the second day she read of the remaining pages plus pages. On the third day she read of the remaining pages plus pages. She then realized that there were only pages left to read, which she read the next day. How many pages are in this book?
小提示：
先倒推额外读的页数，再倒推每天读掉的分数
Undo the extra pages first, then undo the fraction read each day.
大提示：
从第三天后剩下的 页倒推
Work backward from the pages left after the third day.
解答：
第三天后剩下 页。在读最后额外的 页之前，她还剩 页。这是当时剩余页数的 ，所以第三天开始前她剩下 页。
在读第二天额外的 页之前，她还剩 页。这是当时剩余页数的 ，所以第二天开始前她剩下 页。
在读第一天额外的 页之前，她还剩 页。这是当时剩余页数的 ，所以第一天开始前她有 页，也就是全书 页。
所以正确答案是 C。
The pages left after the third day is Before reading the last pages, she had pages left. This is of the pages remaining, so she had pages left before the third day.
Before reading the pages, she had pages left. This is of the pages remaining, so she had pages left before the second day.
Before reading the pages, she had pages left. This is of the pages remaining, so she had pages left before the first day, making the book pages.
Thus, the answer is C .
其他年份的第 21 题
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- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
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