Question

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?

$48$

$87$

$91$

$96$

$120$

Video solution:

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Written solution:

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 $10 \text{ feet} \times 14\text{ feet}.$ 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 Problem 9

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Written solution:

Problem 9 in Other Years