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Question from Svitlana, a student:

Professor Reissig is doing renovations on one of the rectangular-shaped bedrooms in his house. He is putting up a border around the room. The room's length is seven feet more than two-thirds of its width. The area of this bedroom is one hundred eighty square feet. If the border costs $1.25 per six inches, what is the minimum cost for the border?

Svitlana,

The key to this problem is a careful reading of the room's length is seven feet more than two-thirds of its width. If the length is L feet and the width is W feet then you know that L is seven feet more than 2/3 W. That is

L = 2/3 W + 7.

The area of the room is 180 square feet so

L × W = 180.

Substitute L = 2/3 W + 7 into the expression for the area to find an equation for W.

Solve for L and W and this will then allow you to calculate the cost.

Penny

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