AMC 8 2017 Problem 17
AMC8 2017 年第 17 题
方程与不等式★★★☆☆
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?
我有一些金币和若干财宝箱。我尝试在每个财宝箱里放 9 枚金币，那么还剩 2 个财宝箱是空的。若我在每个财宝箱里放 6 枚金币，那么还剩 3 枚金币无处可放。问我有多少枚金币？
- A.9
- B.27
- C.45
- D.63
- E.81
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
After putting 9 9 coins in all but two of the chests, I could take 3 3 coins out of each chest to leave 6 6 coins in those chests. Doing this would allow me to fill the remaining 2 2 chests with 6 6 coins each, and have another 3 3 coins left over. So I must have removed 15 15 coins ( 3 (3 from each of 5 5 chests). Thus I initially had put 9 9 coins into each of 5 5 chests, making for a total of 45 45 coins (and 7 7 chests). OR OR Let 𝑐 c be the number of chests. Then 9 ( 𝑐 − 2 ) = 6 𝑐 + 3 9(c−2)=6c+3. Solving yields 𝑐 = 7 c=7, so the number of coins is 6 ⋅ 7 + 3 = 9 ( 7 − 2 ) = 45 6⋅7+3=9(7−2)=45. Answer: 𝐶 C .
继续练习