SOLUTION: Gwen is planting red tulips in a rectangular flowerbed that is 2 feet longer than it is wide. She plans to surround the tulips with a border of daffodils that is 2 feet wide. If th
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Question 190541: Gwen is planting red tulips in a rectangular flowerbed that is 2 feet longer than it is wide. She plans to surround the tulips with a border of daffodils that is 2 feet wide. If the total area is 224 square feet, and she plants 36 daffodils per square foot, then how many daffodils does she need? Answer by jonvaliente(64) (Show Source):
You can put this solution on YOUR website! Let x=width
. x+2=length ("2 feet longer that it is wide")
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Area with 2-feet border = 224
The 2-feet border will add 4 feet to both width and legth of the flowerbed.
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x+4 = width of the flowerbed with border
x+2+4 or x+6= length of the flowerbed with border
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Area=length x width, so:
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(x+4)*(x+6)=224
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Solving for x, we get:
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Subtracting 224 from both sides we get:
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Factoring, we get:
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x+20=0 and/or x-10=0
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if x+20=0, then:
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x+20-20=0-20 or x=-20
Since the width cannot be negative then this cannot be a solution,
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If x-10=0, then:
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x-10+10=0+10 or x=10
Therefore the width of the flowerbed is 10feet and the length is x+2 or 10+2 or 12 feet
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The area of the flower bed without the border is 10x12=120 square feet
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So the area of the border should be 224-120=104 square feet
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36 daffodils per square foot of border, then 104*36=3744 daffodils
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The answer is 3744 daffodils
