Question

万圣节时 Casper 吃掉了自己糖果的 $\frac{1}{3}$ ，然后给了弟弟 $2$ 颗。第二天，他吃掉剩余糖果的 $\frac{1}{3}$ ，然后给了妹妹 $4$ 颗。第三天，他吃掉最后的 $8$ 颗糖果。Casper 一开始有多少颗糖果？

On Halloween Casper ate $\frac{1}{3}$ of his candies and then gave $2$ candies to his brother. The next day he ate $\frac{1}{3}$ of his remaining candies and then gave $4$ candies to his sister. On the third day he ate his final $8$ candies. How many candies did Casper have at the beginning?

$30$

$39$

$48$

$57$

$66$

答案：A

知识点：分数逆推法

难度评级：1140

解答：

倒推。给妹妹 $4$ 颗之前，Casper 有 $12$ 颗糖果，因为第二天结束时剩 $8$ 颗。

这 $12$ 颗是第一天结束后糖果数的 $\dfrac23$ ，所以第一天结束后有 $18$ 颗。

给弟弟 $2$ 颗之前有 $20$ 颗。这是原来糖果数的 $\dfrac23$ ，所以一开始有 $30$ 颗。

所以正确答案是 A。

Work backward. Before giving $4$ candies to his sister, Casper had $12$ candies, because he ended the second day with $8$ .

Those $12$ candies were $\dfrac23$ of what he had after the first day, so after the first day he had $18$ candies.

Before giving $2$ candies to his brother, he had $20$ candies. This was $\dfrac23$ of his original amount, so he began with $30$ candies.

Thus, A is the correct answer.

2011 AMC 10B 第 6 题

答案：A

难度评级：1140

解答：

其他年份的第 6 题