SOLUTION: a pool measuring 18 meters by 28 meters. if the area of the pool and the path combined is 1200 square meters, what is the width?

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Question 620919: a pool measuring 18 meters by 28 meters. if the area of the pool and the path combined is 1200 square meters, what is the width?
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
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I presume that you want the width of the path.
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Let x be the width of the path.
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The path goes all the way around the pool to the width of the pool plus the path (on both sides) is 18+2x.
The length of the pool plus the path is 28+2x.
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The formula for the area of the pool and the path is length times width. So,
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%2818%2B2x%29%2828%2B2x%29=1200
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Simplify and solve for x.
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504%2B56x%2B36x%2B4x%5E2=1200
4x%5E2%2B92x-696=0
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Divide every term by 4.
x%5E2%2B23-174=0
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We can solve this quadratic by factoring. We need two numbers whose product is -174 and whose sum is 23. The numbers are 29 and -6. The quadratic in factored form is
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%28x-6%29%28x%2B29%29=0
x-6=0 or x%2B29=0 so x=6 or x=-29. We cannot have a path with a negative width, so the pathway is 6 meters wide.
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Hope this helps! Feel free to email if you have question about the solution.
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Ms.Figgy
math.in.the.vortex@gmail.com