2018 AMC 8

Complete problem set with solutions and individual problem pages

Problem 9 Easy

Monica is tiling the floor of her 12-foot by 16-foot living room. She 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 she use?

  • A.

    48

  • B.

    87

  • C.

    89

  • D.

    96

  • E.

    120

Answer:B

Solution 1

She will place (12\cdot2)+(14\cdot2)=52 tiles around the border. For the inner part of the room, we have 10\cdot14=140 square feet. Each tile takes up 4 square feet, so he will use \frac{140}{4}=35 tiles for the inner part of the room. Thus, the answer is 52+35= \boxed{\textbf{(B) }87}.

 

Solution 2

The area around the border: (12 \cdot 2) + (14 \cdot 2) = 52. The area of tiles around the border: 1 \cdot 1 = 1. Therefore, \frac{52}{1} = 52 is the number of tiles around the border.

The inner part will have (12 - 2)(16 - 2) = 140. The area of those tiles are 2 \cdot 2 = 4. \frac{140}{4} = 35 is the amount of tiles for the inner part. So, 52 + 35 = \boxed{87}.

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