Difference between revisions of "2007 AMC 12B Problems/Problem 1"
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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? | 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? | ||
− | <math>\mathrm {(A)} 678 | + | <math>\mathrm{(A)}\ 678 \qquad \mathrm{(B)}\ 768 \qquad \mathrm{(C)}\ 786 \qquad \mathrm{(D)}\ 867 \qquad \mathrm{(E)}\ 876</math> |
==Solution== | ==Solution== | ||
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: | 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: | ||
− | + | <cmath>12*8+12*8+10*8+10*8-60=160+192-60=292</cmath> | |
− | < | ||
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We have three bedrooms, so she must paint <math>292*3=876 \Rightarrow \mathrm {(E)}</math> square feet of wall. | We have three bedrooms, so she must paint <math>292*3=876 \Rightarrow \mathrm {(E)}</math> square feet of wall. | ||
==See Also== | ==See Also== | ||
{{AMC12 box|year=2007|ab=B|before=First question|num-a=2}} | {{AMC12 box|year=2007|ab=B|before=First question|num-a=2}} | ||
+ | [[Category:Introductory Geometry Problems]] |
Revision as of 22:53, 11 July 2009
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?
Solution
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:
We have three bedrooms, so she must paint
square feet of wall.
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 |