AMC8 2017

AMC8 2017 · Q17

AMC8 2017 · Q17. It mainly tests Linear equations, Remainders & modular arithmetic.

Starting with some gold coins and some empty treasure chests, I tried to put 9 gold coins in each treasure chest, but that left 2 treasure chests empty. So instead I put 6 gold coins in each treasure chest, but then I had 3 gold coins left over. How many gold coins did I have?

起始有一些金币和一些空宝箱，我试图每个宝箱放入9枚金币，但剩下2个宝箱为空。所以我改为每个宝箱放入6枚金币，但剩下3枚金币。问我有多少金币？

(A) 9 9

(B) 27 27

(D) 63 63

(E) 81 81

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): After putting 9 coins in all but two of the chests, I could take 3 coins out of each chest to leave 6 coins in those chests. Doing this would allow me to fill the remaining 2 chests with 6 coins each, and have another 3 coins left over. So I must have removed 15 coins (3 from each of 5 chests). Thus I initially had put 9 coins into each of 5 chests, making for a total of 45 coins (and 7 chests).

答案 (C)：在把除了两个箱子之外的所有箱子都各放入 9 枚硬币之后，我可以从每个箱子取出 3 枚，使这些箱子各剩 6 枚。这样就能把剩下的 2个箱子也各装到 6 枚，并且还会多出 3 枚硬币。因此我一定一共取出了 15 枚硬币（从 5 个箱子中每个取 3 枚）。于是最初我在 5 个箱子中各放了 9 枚硬币，进而共有45 枚硬币（并且共有 7 个箱子）。

Topics