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:
A.
B.
C.
D.
E.
Solution:
Note that each square foot of the border would require one tile, meaning that the border will take:
However, notice that this will cause overlapping tiles in each of the four corners, so to fix this, we subtract . Therefore, the border will take:
Since we have removed one foot from each side due to the border, the remaining rectangle is . This must be tiled completely by tiles, so it will take:
As it takes square tiles to tile the border, and square tiles to tile the remaining area, it will take:
Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions