Problem:
Tyler is tiling the floor of his foot by 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?
Answer Choices:
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Solution:
The perimeter of the room is feet. The corner tiles each occupy feet of the perimeter, so Tyler needs those plus another - one-foot square tiles to make the border. The remaining space in the room is a foot by foot rectangle, so Tyler need two-foot square tiles to cover it. Therefore he needs a total tiles.
If Tyler used only one-foot square tiles, he would need a total of tiles. As above, the room minus the border is a foot by foot rectangle to be covered with two-foot square tiles, each of which has the same area as one-foot square tiles. Therefore the number of tiles needed to cover that portion of the room is not but , and the total number of tiles needed is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions