AMC8 2018

AMC8 2018 · Q9

AMC8 2018 · Q9. It mainly tests Fractions, Area & perimeter.

Tyler is tiling the floor of his 12 foot by 16 foot living room. He plans to place one-foot by one-foot square tiles to form a border along the edges of the room and to fill in the rest of the floor with two-foot by two-foot square tiles. How many tiles will he use?

Tyler正在为他12英尺乘16英尺的客厅铺瓷砖。他计划沿房间边缘放置一英尺乘一英尺的方形瓷砖作为边框，并用两英尺乘两英尺的方形瓷砖填充其余地板。他将使用多少块瓷砖？

(A) 48 48

(B) 87 87

(D) 96 96

(E) 120 120

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): The perimeter of the room is $2(12+16)=56$ feet. The $4$ corner tiles each occupy $2$ feet of the perimeter, so Tyler needs those $4$ plus another $56-4\cdot2=48$ one-foot square tiles to make the border. The remaining space in the room is a $10$ foot by $14$ foot rectangle, so Tyler needs $\frac{10}{2}\cdot\frac{14}{2}=35$ two-foot square tiles to cover it. Therefore he needs a total of $4+48+35=87$ tiles.

答案（B）：房间的周长是 $2(12+16)=56$ 英尺。四个角上的瓷砖每块占据周长中的 $2$ 英尺，所以 Tyler 需要这 $4$ 块角砖，再加上另外 $56-4\cdot2=48$ 块边框用的 1 英尺见方瓷砖来铺边框。房间剩余的空间是一个 $10$ 英尺乘 $14$ 英尺的长方形，因此 Tyler 需要 $\frac{10}{2}\cdot\frac{14}{2}=35$ 块边长为 2 英尺的正方形瓷砖来覆盖。于是他总共需要 $4+48+35=87$ 块瓷砖。

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