2018 AMC 8 Problem 9
Attempt Problem 9 of the 2018 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2018 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
9.
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?
Small hint:
Count the -foot border tiles first, being careful not to double-count the corners.
Big hint:
After removing a -foot border, the remaining rectangle is feet by feet.
Video solution:
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Written solution:
Note that each square foot of the border would require one tile, meaning that the border will take tiles. 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 square tiles to completely tile.
Since we have removed one foot from each side due to the border, the remaining rectangle is feet by feet. This must be tiled completely by tiles, so it will take tiles in total to tile this area.
As it takes square tiles to tile the border, and square tiles to tile the remaining area, it will take tiles in total to fill in Tyler’s entire living room floor.
Thus, the correct answer is B.
Problem 9 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
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