Question

Joe 有 $23$ 枚硬币，分别是 $5$ 分、 $10$ 分和 $25$ 分硬币。他的 $10$ 分硬币比 $5$ 分硬币多 $3$ 枚，所有硬币总值为 $320$ 分。Joe 的 $25$ 分硬币比 $5$ 分硬币多多少枚？

Joe has a collection of $23$ coins, consisting of $5$ -cent coins, $10$ -cent coins, and $25$ -cent coins. He has $3$ more $10$ -cent coins than $5$ -cent coins, and the total value of his collection is $320$ cents. How many more $25$ -cent coins does Joe have than $5$ -cent coins?

$0$

$1$

$2$

$3$

$4$

答案：C

知识点：钱币方程组

难度评级：1220

解答：

设 Joe 有 $x$ 枚 $5$ 分硬币，则他有 $x + 3$ 枚 $10$ 分硬币。

因此，他有枚 $25$ 分硬币。 $23 - x - (x + 3) = 20 - 2x$

这些硬币的总价值为 $5x + 10(x + 3) + 25(20 - 2x)$ $= 530 - 35x.$

由总价值可得 $530 - 35x = 320 \Rightarrow x = 6.$

所以 Joe 有 $20 - 2 \cdot 6 = 8$ 枚 $25$ 分硬币；他的 $25$ 分硬币比 $5$ 分硬币多 $8 - 6 = 2$ 枚。

因此正确答案是 C。

Let $x$ be the number of $5$ -cent coins that Joe has. Then the number of $10$ -cent coins he has is $x + 3.$

Therefore, Joe has $23 - x - (x + 3) = 20 - 2x$ $25$ -cent coins.

The total value of all these coins is $5x + 10(x + 3) + 25(20 - 2x)$ $= 530 - 35x.$

We know that $530 - 35x = 320 \Rightarrow x = 6.$

This means that Joe has $20 - 2 \cdot 6 = 8$ $25$ -cent coins. Therefore, he has $8 - 6 = 2$ more $25$ -cent coins than $5$ -cent coins.

Thus, C is the correct answer.

2018 AMC 10A 第 8 题

答案：C

难度评级：1220

解答：

其他年份的第 8 题