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 ft by 24 ft and the area of the rug is 153 sqft, how wide will the border be?

Algebra ->  Rectangles -> 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 ft by 24 ft and the area of the rug is 153 sqft, how wide will the border be?       Log On


   

Question 314933: 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 ft by 24 ft and the area of the rug is 153 sqft, how wide will the border be?
a=w*l, a=16*24 = 384 ft ?
wouldn't you just subtract the 153 from the 384, then divide by four?
Answer by CharlesG2(834) 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 16 ft by 24 ft and the area of the rug is 153 sqft, how wide will the border be?
a=w*l, a=16*24 = 384 ft ?
wouldn't you just subtract the 153 from the 384, then divide by four?"
room is 16 ft by 24 ft
room area = 16 * 24 = 384 square feet
rug area = 153 square feet
area border = room area - rug area
area border = 384 - 153 = 231 square feet
area border = w * 16 + w * 16 + w(24 - 2w) + w(24 - 2w) = 231
area border = 32w + 24w - 2w^2 + 24w - 2w^2 = 231
area border = 32w + 48w - 4w^2 = 231
-4w^2 + 80w - 231 = 0
w^2 - 20w + 57.75 = 0
a = 1, b = -20, c = 57.75
w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
w+=+%2820+%2B-+sqrt%28+400+-+4%2857.75%29+%29%29%2F2+
w+=+%2820+%2B-+sqrt%28400+-+231%29%29%2F2+
w+=+%2820+%2B-+sqrt%28169%29%29%2F2+
w+=+%2820+%2B-+13%29%2F2+
w1 = (20 + 13)/2 = 33/2 = 16.5, which makes no sense
w2 = (20 - 13)/2 = 7/2 = 3.5, so border width is 3.5
check:
2 * (3.5*16) + 2 * (3.5 * (24-7))
2 * 56 + 2 * (3.5 * 17)
112 + 2(59.5)
112 + 119
231
(dividing 231 by 4, would give you 57.75)