AMC12 2007 B

AMC12 2007 B · Q1

AMC12 2007 B · Q1. It mainly tests Fractions, Area & perimeter.

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 的房子有 $3$ 个卧室。每个卧室长 $12$ 英尺，宽 $10$ 英尺，高 $8$ 英尺。Isabella 必须粉刷所有卧室的墙壁。每个卧室的门窗（不需粉刷）占用 $60$ 平方英尺。必须粉刷多少平方英尺的墙壁？

(A) 678 678

(B) 768 768

(D) 867 867

(E) 876 876

Answer

Correct choice: (E)

正确答案：（E）

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.

每个卧室有四面墙（她不能粉刷地板或天花板）。因此，我们计算一个卧室的墙壁面积： \[2\cdot(12\cdot8+10\cdot8)-60=2\cdot176-60=292\] 共有三个卧室，所以她必须粉刷 $292\cdot3=\boxed{\textbf{(E) }876}$ 平方英尺的墙壁。

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