Question

三位慷慨的朋友各有一些现金，并按如下方式重新分配：Ami 给 Jan 和 Toy 足够的钱，使他们各自的钱数加倍。然后 Jan 给 Ami 和 Toy 足够的钱，使他们各自的钱数加倍。最后 Toy 给 Ami 和 Jan 足够的钱，使他们各自的钱数加倍。如果 Toy 开始时有 $\$36$ ，结束时也有 $\$36$ ，那么三位朋友一共有多少钱？

Three generous friends, each with some cash, redistribute their money as follows: Ami gives enough money to Jan and Toy to double the amount that each has. Jan then gives enough to Ami and Toy to double their amounts. Finally, Toy gives Ami and Jan enough to double their amounts. If Toy has $\$36$ when they begin and $\$36$ when they end, what is the total amount that all three friends have?

$\$108$

$\$180$

$\$216$

$\$252$

$\$288$

答案：D

知识点：逆推法不变量

难度评级：1620

解答：

Toy 开始有 $\$36$ 。Ami 使 Toy 的钱加倍后，Toy 有 $\$72$ 。Jan 再使 Toy 的钱加倍后，Toy 有 $\$144$ 。

Toy 最后结束时有 $\$36$ ，所以 Toy 给出了 $\$144-\$36=\$108$ 。这笔钱使 Ami 和 Jan 的总钱数加倍，因此 Toy 最后行动前 Ami 和 Jan 合计有 $\$108$ 。

总钱数不变，所以总数是 $\$144+\$108=\$252$ 。

所以正确答案是 D。

Toy begins with $\$36$ . After Ami doubles Toy's amount, Toy has $\$72$ . After Jan doubles Toy's amount, Toy has $\$144$ .

On Toy's final turn, Toy ends with $\$36$ , so Toy gives away $\$144-\$36=\$108$ . That gift doubles the combined amount of Ami and Jan, so Ami and Jan together had $\$108$ just before Toy's final turn.

The total amount of money is constant, so the total is $\$144+\$108=\$252$ .

Thus, the correct answer is D .

1998 AMC 8 第 25 题

答案：D

难度评级：1620

解答：

其他年份的第 25 题