Question

我有一些金币和一些空宝箱。我试着每个宝箱放 $9$ 枚金币，但这样会剩下 $2$ 个宝箱空着。于是我改为每个宝箱放 $6$ 枚金币，但这样会剩下 $3$ 枚金币。我有多少枚金币？

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?

$9$

$27$

$45$

$63$

$81$

答案：C

知识点：方程组

难度评级：1240

小提示：

设宝箱数为 $n$

Let $n$ be the number of treasure chests.

大提示：

为每箱 $9$ 枚的尝试和每箱 $6$ 枚的尝试分别写方程

Write one equation for the $9$ -coins attempt and another for the $6$ -coins attempt.

视频讲解：

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文字解答：

设宝箱数为 $n$ ，金币数为 $g$ 。那么 $9(n - 2) = g$ 且 $6n + 3 = g\text{。}$ 解这个方程组得 $n = 7$ ，所以金币数为 $6 \cdot 7 + 3 = 45$ 。

所以正确答案是 C。

Let $n$ be the number of treasure chests and $g$ be the number of gold coins. Then $9(n - 2) = g$ and $6n + 3 = g.$ Solving this system yields $n = 7,$ so the number of gold coins is $6 \cdot 7 + 3 = 45.$

Thus, C is the correct answer.

2017 AMC 8 第 17 题