2011 AMC 10B 第 6 题

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

小提示：

从最后的

8

颗糖果倒推。

Work backward from the final

8

candies

大提示：

给妹妹

4

颗之前有

12

颗，这是前一数量的三分之二。

Before giving away

4

, Casper had

12

, which was two thirds of the previous amount

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