Difference between revisions of "2018 AMC 8 Problems/Problem 9"

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He will place <math>(12\cdot2)+(14\cdot2)=52</math> tiles around the border. For the inner part of the room, we have <math>10\cdot14=140</math> square feet. Each tile takes up <math>4</math> square feet, so he will use <math>\frac{140}{4}=35</math> tiles for the inner part of the room. Thus, the answer is <math>52+35=\boxed{\textbf{(B) }87}</math>
 
He will place <math>(12\cdot2)+(14\cdot2)=52</math> tiles around the border. For the inner part of the room, we have <math>10\cdot14=140</math> square feet. Each tile takes up <math>4</math> square feet, so he will use <math>\frac{140}{4}=35</math> tiles for the inner part of the room. Thus, the answer is <math>52+35=\boxed{\textbf{(B) }87}</math>
 
==Solution 2==
 
==Solution 2==
The area around the border: (12 * 2) + (14 * 2) = 52. The area of tiles around the border: 1 * 1 = 1. Therefore, 52/1 = 52 is the number of tiles around the border.
+
The area around the border: <math>(12 \cdot 2) + (14 \cdot 2) = 52</math>. The area of tiles around the border: <math>1 \cdot 1 = 1</math>. Therefore, <math>\frac{52}{1} = 52</math> 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 * 2 = 4. 140/4 = 35 is the amount of tiles for the inner part. So, 52 + 35 = 87
+
The inner part will have <math>(12 - 2)(16 - 2) = 140</math>. The area of those tiles are <math>2 \cdot 2 = 4</math>. <math>\frac{140}{4} = 35</math> is the amount of tiles for the inner part. So, <math>52 + 35 = 87</math>.
  
 
==See Also==
 
==See Also==

Revision as of 13:44, 15 July 2019

Problem 9

Tyler is tiling the floor of his 12 foot by 16 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?


$\textbf{(A) }48\qquad\textbf{(B) }87\qquad\textbf{(C) }91\qquad\textbf{(D) }96\qquad \textbf{(E) }120$

Solution

He 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, $52 + 35 = 87$.

See Also

2018 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
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All AJHSME/AMC 8 Problems and Solutions

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