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

Latest revision as of 11:22, 23 January 2024

Problem

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?

$\textbf{(A) }48\qquad\textbf{(B) }87\qquad\textbf{(C) }89\qquad\textbf{(D) }96\qquad \textbf{(E) }120$

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, $52 + 35 = \boxed{87}$ .

Video Solution (CRITICAL THINKING!!!)

https://youtu.be/qJyITbOffGo

~Education, the Study of Everything

Video Solution

https://youtu.be/V5h00z5MDEI

~savannahsolver

@@ Line 1: / Line 1: @@
-==Problem 9==
+==Problem==
-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?
+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?
-==Solution==
-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 4 square feet, so he will use <math>\frac{140}{4}=35</math> tiles for in inner part of the room. Thus, the answer is <math>52+35=\boxed{\textbf{(B) }87}</math>
+<math>\textbf{(A) }48\qquad\textbf{(B) }87\qquad\textbf{(C) }89\qquad\textbf{(D) }96\qquad \textbf{(E) }120</math>
+==Solution 1==
-<math>\textbf{(A) }48\qquad\textbf{(B) }87\qquad\textbf{(C) }91\qquad\textbf{(D) }96\qquad \textbf{(E) }120</math>
+She 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==
+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 <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 = \boxed{87}</math>.
+== Video Solution (CRITICAL THINKING!!!)==
+https://youtu.be/qJyITbOffGo
+~Education, the Study of Everything
+==Video Solution==
+https://youtu.be/V5h00z5MDEI
+~savannahsolver
+==See Also==
 {{AMC8 box|year=2018|num-b=8|num-a=10}}

2018 AMC 8 (Problems • Answer Key • Resources)
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