October 27, 2011

Tiling word problem

Someone sent me this problem to solve, so here goes:


Photo courtesy of Brajeshwar
Square polystyrene tiles, 50 cm by 50 cm, are used to cover the ceiling of a classroom measuring 7.4 m by 4.5 m

1. Find the number of tiles that are needed.

2. Find the total cost if one tile costs $130.

Now, consider the room that is 7.4 m by 4.5 m. The tiles will not fit exactly along the 7.4-meter side, so we will need to cut some of the tiles. So we might as well consider it to be 7.5-meter side for the purpose of figuring how many tiles we need.

Along the 7.5 meter side we would need 15 tiles, each 0.5 m. Why? Because 0.5 fits into 7.5 exactly 15 times. It's essentially a division problem... 7.5 ÷ 0.5 but you can solve it mentally by thinking that each meter takes 2 tiles, so 7.5 meters takes 7.5 x 2 = 15 tiles.

Similarly, along the 4.5 meter side you would need 9 tiles, each 0.5 m.

Therefore in total we need 15 x 9 = 135 tiles. Some of those will need cut!

The cost will be 135 x $130 = $17,550. This would be expensive tiling... but I realize the person sending the question might have used some other kind of money units (not US dollars)!

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