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2007 AMC 10B Problem 1

Problem 1 of 25EasierGeometry

Isabella’s house has 33 bedrooms. Each bedroom is 1212 feet long, 1010 feet wide, and 88 feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy 6060 square feet in each bedroom. How many square feet of walls must be painted?

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Solution

The walls of one bedroom have area 2(12+10)⋅8=44⋅8=3522(12+10)\cdot 8 = 44\cdot 8 = 352 square feet. Subtracting the 6060 square feet of doorways and windows leaves 352−60=292352-60=292 square feet per bedroom. With 33 bedrooms, the total is 3⋅292=8763\cdot 292 = 876 square feet. Thus, the correct answer is E.
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