Question

Trickster Rabbit 同意每次 Foolish Fox 经过 Rabbit 家旁边的桥时，都把 Fox 的钱翻倍，但 Fox 每次过桥后必须向 Rabbit 支付 $40$ 枚硬币的过路费。付款在翻倍之后进行。Fox 起初很高兴，但他发现自己过桥三次后钱全没了。Fox 一开始有多少枚硬币？

Trickster Rabbit agrees with Foolish Fox to double Fox's money every time Fox crosses the bridge by Rabbit's house, as long as Fox pays $40$ coins in toll to Rabbit after each crossing. The payment is made after the doubling. Fox is excited about his good fortune until he discovers that all his money is gone after crossing the bridge three times. How many coins did Fox have at the beginning?

$20$

$30$

$35$

$40$

$45$

答案：C

知识点：逆推法

难度评级：1070

解答：

最后 Fox 有 $0$ 枚硬币，所以第三次付过路费之前有 $40$ 枚。

因此第三次翻倍前有 $40 \div 2 = 20$ 枚；第二次付过路费之前有 $20 + 40 = 60$ 枚。

第二次翻倍前有 $60 \div 2 = 30$ 枚；第一次付过路费之前有 $30 + 40 = 70$ 枚。

最后，第一次翻倍前 Fox 有 $70 \div 2 = 35$ 枚硬币。

所以正确答案是 C。

We know that Fox has $0$ coins at the end. Then before paying the final toll, Fox had $40$ coins.

Then he had $40 \div 2 = 20$ coins before the doubling. Then before paying the toll for the second crossing, he had $20 + 40 = 60$ coins.

Before the doubling on the second crossing, he had $60 \div 2 = 30$ coins. On the first crossing before the toll, Fox had $30 + 40 = 70$ coins.

Finally, before the first doubling, Fox had $70 \div 2 = 35$ coins.

Thus, the correct answer is C .

2016 AMC 10A 第 8 题

答案：C

难度评级：1070

解答：

其他年份的第 8 题