AMC10 2016 A

AMC10 2016 A · Q8

AMC10 2016 A · Q8. It mainly tests Manipulating equations, Interest / growth (simple).

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?

狡猾的兔子与愚蠢的狐狸约定：狐狸每次经过兔子家旁的桥时，兔子都会把狐狸的钱翻倍，但条件是狐狸在每次过桥后要付给兔子 40 枚金币作为过桥费。付款发生在翻倍之后。狐狸为自己的好运而兴奋，直到他发现自己过桥三次后钱全部没了。狐狸最开始有多少枚金币？

(A) 20 20

(B) 30 30

(D) 40 40

(E) 45 45

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): Working backwards, Fox must have approached the bridge for the third time with 20 coins in order to have no coins left after paying the toll. In the second crossing he must have started with 30 coins in order to have $20+40=60$ before paying the toll. So he must have started with 35 coins in order to have $30+40=70$ before paying the toll for the first crossing.

答案（C）：倒推可知，狐狸第三次走到桥边时必须带着20枚硬币，这样在支付通行费后才会一枚不剩。第二次过桥时，他必须从30枚硬币开始，这样在付费前会有$20+40=60$枚硬币。因此第一次过桥前，他必须从35枚硬币开始，这样在付第一次通行费之前会有$30+40=70$枚硬币。

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