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| Math Central | Quandaries & Queries |
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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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