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Difference between revisions of "2007 AMC 12B Problems/Problem 1"
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==Problem==
 
==Problem==
  
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Isabella's house has 3 bedrooms. Each bedroom is 12 feet long, 10 feet wide, and 8 feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy 60 square feet in each bedroom. How many square feet of walls must be painted?  
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Isabella's house has <math>3</math> bedrooms. Each bedroom is <math>12</math> feet long, <math>10</math> feet wide, and <math>8</math> feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy <math>60</math> square feet in each bedroom. How many square feet of walls must be painted?  
  
 
<math>\mathrm{(A)}\ 678 \qquad \mathrm{(B)}\ 768 \qquad \mathrm{(C)}\ 786 \qquad \mathrm{(D)}\ 867 \qquad \mathrm{(E)}\ 876</math>
 
<math>\mathrm{(A)}\ 678 \qquad \mathrm{(B)}\ 768 \qquad \mathrm{(C)}\ 786 \qquad \mathrm{(D)}\ 867 \qquad \mathrm{(E)}\ 876</math>
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==Solution==
 
==Solution==
  
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There are four walls in each bedroom, since she can't paint floors or ceilings. So we calculate the number of square feet of wall there is in one bedroom:
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There are four walls in each bedroom (she can't paint floors or ceilings). Therefore, we calculate the number of square feet of walls there is in one bedroom:
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<cmath>(12*8)+(12*8)+(10*8)+(10*8)-60=160+192-60=292</cmath>
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<cmath>2\cdot(12\cdot8+10\cdot8)-60=2\cdot176-60=292</cmath>
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We have three bedrooms, so she must paint <cmath>292*3=876 \Rightarrow \fbox{(E)}</cmath> square feet of wall.
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We have three bedrooms, so she must paint <math>292\cdot3=\boxed{\textbf{(E) }876}</math> square feet of walls.
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~MathFun1000
  
 
==See Also==
 
==See Also==

Latest revision as of 09:19, 7 March 2022

The following problem is from both the 2007 AMC 12B #1 and 2007 AMC 10B #1, so both problems redirect to this page.

Problem

Isabella's house has $3$ bedrooms. Each bedroom is $12$ feet long, $10$ feet wide, and $8$ feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy $60$ square feet in each bedroom. How many square feet of walls must be painted?

$\mathrm{(A)}\ 678 \qquad \mathrm{(B)}\ 768 \qquad \mathrm{(C)}\ 786 \qquad \mathrm{(D)}\ 867 \qquad \mathrm{(E)}\ 876$

Solution

There are four walls in each bedroom (she can't paint floors or ceilings). Therefore, we calculate the number of square feet of walls there is in one bedroom: \[2\cdot(12\cdot8+10\cdot8)-60=2\cdot176-60=292\] We have three bedrooms, so she must paint $292\cdot3=\boxed{\textbf{(E) }876}$ square feet of walls.

~MathFun1000

See Also

2007 AMC 12B (Problems • Answer Key • Resources)
Preceded by
First question 		Followed by
Problem 2
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 AMC 12 Problems and Solutions
2007 AMC 10B (Problems • Answer Key • Resources)
Preceded by
First Problem 		Followed by
Problem 2
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 AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

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