Question 67506This question is from textbook
: a landscape architect has included a rectangular flower bed measuring 9ft by 5ft in her plans for a new building. She wants to use two colors of flowers in the bed, one in the center and the other for a border of the same with on all four sides. If she had enough plants to cover 24ft^2 for the border, how wide can the border be?
This question is from textbook
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! :
Cutting through all this nonsense about flowers and architects, the problem appears to be: In a 9' by 5' plot, how wide a border would cover 24 sq ft?
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The total area: 9 * 5 = 45 sq ft: Middle area = 45 - 24 = 21 sq ft
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Let x = width of the border
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Use the area of the middle to find the value of x:
(9-2x)(5-2x) = 21
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45 - 28x + 4x^2 = 21
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4x^2 - 28x + 45 - 21 = 0
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4x^2 - 28x + 24 = 0
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Simplify, divide equation by 4
x^2 - 7x + 6 = 0
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Factors to:
(x-6)(x-1) = 0
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x = 6 and x = 1
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x = 1 ft is the solution that makes sense
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To check our solution; Find the area of the center
(9-2)*5-2) = 21 sq ft
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Remaining: 45 - 21` = 24 sq ft the area of the border
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