AMC10 2015 A

AMC10 2015 A · Q2

AMC10 2015 A · Q2. It mainly tests Linear equations, Area & perimeter.

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?

一个盒子里有一些三角形和正方形瓷砖。盒子里总共有 25 块瓷砖，总边数为 84 条。有多少块正方形瓷砖？

(A) 3 3

(B) 5 5

(D) 9 9

(E) 11 11

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): Counting 3 edges per tile gives a total of $3 \cdot 25 = 75$ edges, and exactly 1 edge per square tile is missing. So there are exactly $84 - 75 = 9$ square tiles.

答案（D）：按每块拼块有 $3$ 条边来计数，总共有 $3 \cdot 25 = 75$ 条边，并且每个正方形拼块恰好缺少 $1$ 条边。因此正方形拼块的数量恰为 $84 - 75 = 9$。

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