SOLUTION: Width of border: rectangular flower bed 9' by 5'. 2 colors in the bed, one in center, one for border of the same width on all sides. If she has enough plants to cover 24 ft^2 fo

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Question 151319This question is from textbook
: Width of border: rectangular flower bed 9' by 5'. 2 colors in the bed, one in center, one for border of the same width on all sides. If she has enough plants to cover 24 ft^2 for the border, how wide can the border be? This question is from textbook

Found 2 solutions by scott8148, stanbon:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
area of flower bed is 45 ft^2 (9*5) __ area of center is 21 ft^2 (45-24)

let x="width of border" __ so center length is 9-2x and center width is 5-2x

(9-2x)(5-2x)=21 __ FOILing __ 45-28x+4x^2=21 __ subtracting 21 __ 4x^2-28x+24=0 __ dividing by 4 __ x^2-7x+6=0

factoring __ (x-6)(x-1)=0

x-6=0 __ x=6 __ greater than width of entire bed, so not realistic

x-1=0 __ x=1

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Width of border: rectangular flower bed 9' by 5'. 2 colors in the bed, one in center, one for border of the same width on all sides. If she has enough plants to cover 24 ft^2 for the border, how wide can the border be?
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Let the width be "x":
Area of the border ?
Draw the picture.
Top and bottom areas: (5+2x)x = 5x + 2x^2
Left and right side areas : 9x
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Area Equation:
2(2x^2+5x) + 2(9x) = 24
4x^2 + 28x - 24 = 0
x^2 + 7x -6 = 0
(x+6)(x-1) = 0
Positive solution:
x = 1 ft (the width of the border should be 1 ft)
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Cheers,
Stan H.