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The floor of a basement game room is covered by 480 square asphalt tiles of a certain size. If 3 inches is added to the length of a side of each tile, the floor could be covered by 270 tiles. Find the length of a side of the tile on the floor.
Solution

Even though the number of tiles changes the floor area did not change. Thus $$A_f = 480A_1 = 270 A_2$$

Where $$A_1$$ is the area of a tile from the original tile and $$A_2$$ is the area of one tile afted the addition of 3 inches.

Thus if $$x$$ is the side of one tile, then the second is $$x+3$$.

$$480A_1 = 270A_2$$

$$48(x^2) = 27(x+3)^2$$

$$\frac{4}{3}x = x+3$$

$$\frac{1}{3} x= 3$$

$$x = 9$$ inches

Thus the lenght of a side of the tile is 9 inches.