2007 AMC 10B Problem 1

Question

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

Each bedroom has four walls; find the total wall area from the perimeter and the height

Multiply the room’s perimeter by its height, then subtract

60

The walls of one bedroom have area

2(12+10)\cdot 8 = 44\cdot 8 = 352

square feet. Subtracting the

60

square feet of doorways and windows leaves

352-60=292

square feet per bedroom.

With

3

bedrooms, the total is

3\cdot 292 = 876

square feet.

Thus, the correct answer is E.

Problem 1 in other years