Question

Tyler 正在给他十二英尺乘十六英尺的客厅铺地砖。他计划沿房间边缘用一英尺乘一英尺的正方形地砖铺一圈边框，其余部分用二英尺乘二英尺的正方形地砖铺满。他一共会用多少块地砖？

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?

$48$

$87$

$91$

$96$

$120$

答案：B

知识点：铺砖面积

难度评级：1100

视频讲解：

Click to load, then click again to play

文字解答：

注意边框每平方英尺需要一块地砖，所以四边相加会得到 $16+12+16+12=56$ 块。不过这样四个角各重复计算了一次，所以要减去 $4$ 。因此边框共需要 $56-4=52$ 块 $1\times 1$ 正方形地砖。

由于每边都去掉了一英尺宽的边框，剩下的内部矩形为 $10$ 英尺乘 $14$ 英尺。它要完全铺上 $2 \times 2$ 的地砖，所以需要块。 $\dfrac{10\cdot14}{2\cdot2} = 35$

边框需要 $52$ 块 $1\times 1$ 地砖，内部需要 $35$ 块 $2\times 2$ 地砖，因此一共需要 $52+35=87$ 块地砖。

所以正确答案是 B。

Note that each square foot of the border would require one tile, meaning that the border will take $16+12+16+12=56$ tiles. However, notice that this will cause overlapping tiles in each of the four corners, so to fix this, we subtract $4.$ Therefore, the border will take $56-4=52$ $1\times 1$ square tiles to completely tile.

Since we have removed one foot from each side due to the border, the remaining rectangle is $10$ feet by $14$ feet. This must be tiled completely by $2 \times 2$ tiles, so it will take $\dfrac{10\cdot14}{2\cdot2} = 35$ tiles in total to tile this area.

As it takes $52$ $1\times 1$ square tiles to tile the border, and $35$ $2\times 2$ square tiles to tile the remaining area, it will take $52+35=87$ tiles in total to fill in Tyler's entire living room floor.

Thus, the correct answer is B.

2018 AMC 8 第 9 题

答案：B

难度评级：1100

视频讲解：

文字解答：

其他年份的第 9 题