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 15 feet by 23 feet and the of the rug is 240 square feet, jpow wide will the bord

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Question 330744: 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 15 feet by 23 feet and the of the rug is 240 square feet, jpow wide will the border be?
Answer by ankor@dixie-net.com(22740) About Me  (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 15 feet by 23 feet and the of the rug is 240 square feet,
How wide will the border be?
:
Let x = the width of the border
Then the dimensions of the rug will be: (15-2x) by (23-2x)
The area:
(15-2x) * (23-2x) = 240
FOIL
345 - 30x - 46x + 4x^2 = 240
Arrange as a quadratic equation
4x^2 - 76x + 345 - 240 = 0
:
4x^2 - 76x + 105 = 0
two solutions
(2x - 3)(2x - 35) = 0
only one solution makes sense
2x = 3
x = 1.5 ft border around the rug
:
:
Check solution: (15-3) * (23-3) = 240