SOLUTION: Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution. A rug is to fit in a room so that a border of even width is left on all fou

Question 301257: Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution.
A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 16 feet by 24 feet and the area of the rug is 153 square feet, how wide will the border be? Show work

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 16 feet by 24 feet and the area of the rug is 153 square feet, how wide will the border be? Show work
let the even width border be x feet
If you reduce the width and length of the rug by 2x then you get the length and width of the rug. ( x width on both sides has to be reduced = 2x)
The width of the rug will be 16-2x
The length of the rug will be 24-2x
(16-2x)(24-2x) = 153 ( area of the rug )
384 - 32x-48x+4x^2 = 153
4x^2-80x + 231
by solving for roots x1 & x2
x= 16.5 or 3.5
So the width of the rug will be 16-7 = 9 feet
the length will be 24-7= 17 feet

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