Difference between revisions of "2018 AMC 8 Problems/Problem 9"
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| − | ==Problem | + | ==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? | |
| − | <math>\textbf{(A) }48\qquad\textbf{(B) }87\qquad\textbf{(C) } | + | <math>\textbf{(A) }48\qquad\textbf{(B) }87\qquad\textbf{(C) }89\qquad\textbf{(D) }96\qquad \textbf{(E) }120</math> |
==Solution 1== | ==Solution 1== | ||
| − | + | 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== | ==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 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 = 87</math>. | + | 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== | ==See Also== | ||
{{AMC8 box|year=2018|num-b=8|num-a=10}} | {{AMC8 box|year=2018|num-b=8|num-a=10}} | ||
Latest revision as of 11:22, 23 January 2024
Contents
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?
Solution 1
She will place 
tiles around the border. For the inner part of the room, we have 
square feet. Each tile takes up 
square feet, so he will use 
tiles for the inner part of the room. Thus, the answer is 
.
Solution 2
The area around the border: 
. The area of tiles around the border: 
. Therefore, 
is the number of tiles around the border.
The inner part will have 
. The area of those tiles are 
. 
is the amount of tiles for the inner part. So, 
.
Video Solution (CRITICAL THINKING!!!)
~Education, the Study of Everything
Video Solution
~savannahsolver
See Also
| 2018 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
