2015 AMC 10A 第 2 题

Question

一个盒子里装有三角形瓷砖和正方形瓷砖，共

25

块。这些瓷砖一共有

84

条边。盒子里有多少块正方形瓷砖？

A box contains a collection of triangular and square tiles. There are

25

tiles in the box, containing

84

edges total. How many square tiles are there in the box?

3

5

7

9

11

知识点：方程组

与全部都是三角形瓷砖的情况比较。

Compare the total to the case where all tiles are triangular

每块正方形瓷砖比三角形瓷砖多贡献一条边。

Each square contributes one more edge than a triangle

设三角形瓷砖有

x

块，正方形瓷砖有

y

块，则

x + y = 25

且

3x + 4y = 84\text{。}

把第一个方程乘以

3

，得到

3x + 3y = 75\text{，}

两式相减得

y = 9

。

所以正确答案是 D。

Let

x

be the number of triangular tiles and

y

be the number of square tiles. We then have that

x + y = 25

and

3x + 4y = 84.

Multiplying the first equation by

3

gives us

3x + 3y = 75

and subtracting this from the other equation gives us

y = 9.

Thus, D is the correct answer.

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