A rectangular tiled floor consists of 70 square tiles.

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A rectangular tiled floor consists of 70 square tiles. The rectangular floor is being rearranged so that 2 tiles will be removed from each row of tiles and 4 more rows of tiles will be added. After the change in layout, the floor will still have 70 tiles, and it will still be a rectangle. How many rows were in the tile floor before the change in layout?

Let's set
r = initial rows of tiles
t = initial tiles in each row
so
r*t = 70

Then we take away 2 from each row (t - 2) and add 4 rows (r + 4). We still have 70 tiles, so
(r+4)(t-2) = 70.
rt - 2r + 4t - 8 = 70

Plugging in 70 for rt and 70/r for t (rt = 70 --> t = 70/r):
70 - 2r + 4(70/r) - 8 = 70
2r - 280/r + 8 = 0
r - 140/r + 4 = 0
r^2 + 4r - 140 = 0
(r - 10)(r + 14) = 0
r = 10 ; r = -14

Since we can't have a negative number of rows, the original number of rows (r) must be 10.