2007 AMC 12B Problem 1

Below is the professionally curated solution for Problem 1 of the 2007 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 12B solutions, or check the answer key.

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Concepts:perimeter area

Difficulty rating: 900

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?

$678$

$768$

$786$

$867$

$876$

Solution:

The perimeter of each bedroom floor is $2(12+10)=44$ feet.

So the wall area in one bedroom is $44\cdot8-60=352-60=292$ square feet. Across all three bedrooms, Isabella paints $3\cdot292=876$ square feet.

Thus, the correct answer is E.

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