Difference between revisions of "2007 AMC 12B Problems/Problem 1"
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==Problem== | ==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? | + | 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== | ||
| − | There are four walls in each bedroom | + | 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: |
| − | <cmath>12 | + | <cmath>2\cdot(12\cdot8+10\cdot8)-60=2\cdot176-60=292</cmath> |
| − | We have three bedrooms, so she must paint <math>292 | + | We have three bedrooms, so she must paint <math>292\cdot3=\boxed{\textbf{(E) }876}</math> square feet of walls. |
| + | |||
| + | ~MathFun1000 | ||
==See Also== | ==See Also== | ||
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{{AMC10 box|year=2007|ab=B|before=First Problem|num-a=2}} | {{AMC10 box|year=2007|ab=B|before=First Problem|num-a=2}} | ||
[[Category:Introductory Geometry Problems]] | [[Category:Introductory Geometry Problems]] | ||
| + | {{MAA Notice}} | ||
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 
bedrooms. Each bedroom is 
feet long, 
feet wide, and 
feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy 
square feet in each bedroom. How many square feet of walls must be painted?
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:
![\[2\cdot(12\cdot8+10\cdot8)-60=2\cdot176-60=292\]](http://latex.artofproblemsolving.com/3/1/3/31353e229cf81ff75c2ec4f126826a7b24eb31b6.png)
We have three bedrooms, so she must paint 
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. 
