Question

Hui 很爱读书。她买了一本畅销书 Math is Beautiful。第一天，Hui 读了全书页数的 $1 / 5$ 又多读 $12$ 页；第二天，她读了剩余页数的 $1 / 4$ 又多读 $15$ 页；第三天，她读了剩余页数的 $1 / 3$ 又多读 $18$ 页。随后她发现只剩 $62$ 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 $1 / 5$ 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?

$\ 120$

$\ 180$

$\ 240$

$\ 300$

$\ 360$

答案：C

知识点：分数逆推法

难度评级：1520

解答：

第三天后剩下 $62$ 页。在读最后额外的 $18$ 页之前，她还剩 $80$ 页。这是当时剩余页数的 $\dfrac 23$ ，所以第三天开始前她剩下 $120$ 页。

在读第二天额外的 $15$ 页之前，她还剩 $120+15=135$ 页。这是当时剩余页数的 $\dfrac 34$ ，所以第二天开始前她剩下 $180$ 页。

在读第一天额外的 $12$ 页之前，她还剩 $180+12=192$ 页。这是当时剩余页数的 $\dfrac 45$ ，所以第一天开始前她有 $240$ 页，也就是全书 $240$ 页。

所以正确答案是 C。

The pages left after the third day is $62.$ Before reading the last $18$ pages, she had $80$ pages left. This is $\dfrac 23$ of the pages remaining, so she had $120$ pages left before the third day.

Before reading the $15$ pages, she had $120+15=135$ pages left. This is $\dfrac 34$ of the pages remaining, so she had $180$ pages left before the second day.

Before reading the $12$ pages, she had $180+12=192$ pages left. This is $\dfrac 45$ of the pages remaining, so she had $240$ pages left before the first day, making the book $240$ pages.

Thus, the answer is C .

2010 AMC 8 第 21 题

答案：C

难度评级：1520

解答：

其他年份的第 21 题