2018 AMC 10A 第 8 题

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

小提示：

设

5

分硬币的枚数为

x

。

Let the number of

5

-cent coins be

x

大提示：

同时利用硬币总数和总价值列方程。

Use both the total number of coins and total value equations

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

23 - x - (x + 3) = 20 - 2x

枚

25

分硬币。

这些硬币的总价值为

5x + 10(x + 3) + 25(20 - 2x)

= 530 - 35x\text{。}

由总价值可得

530 - 35x = 320 \Rightarrow x = 6\text{。}

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

小提示：

大提示：

解答：

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