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    Topics || Problems

    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.

    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.