Question 66863: A woman has a flower bed measuring 9 feet by 5 feet in her backyard. She wants to use two colors of flowers in the bed, one in the center and the other for a border of the same width on all four sides. If she has enough plants to cover 24 square feet for the border, how wide can the border be?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website!
I AM ASSUMING THAT THE BORDER IS INSIDE THE 9X5 FLOWER BED.
Let x= the width of the border
Area of the flower bed plus border =9*5=45 sq ft
Length of the flower bed less the border is 9-2x
Width of the flower bed less the border is 5-2x
Area of flower bed less the border is (9-2x)(5-2x)
So our equation is:
45-(9-2x)(5-2x)=24 multiplying out
45-45+28x-4x^2=24 subtract 24 from both sides and multiply by -1
4x^2-28x+24=0 divide by 4
x^2-7x+6=0 It can be factored:
(x-6)(x-1)=0
x=6 ft width of border
or
x=1 ft width of border
CK
border is 6 ft----Length, less border, is 9-2x=9-12=-3
DOESN'T WORK GIVES NEGATIVE LENGTHS
Border is 1 ft----Length,less border, is 9-2=7 ft
Width, less border, is 5-2-------------3 ft
Area, less border, is 3*7=21 sq ft
Area of border 45 sq ft -21 sq ft =24 sq ft
Hope this helps ----ptaylor
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