SOLUTION: A picture 11 inches by 15 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be if the area of t

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Question 115522: A picture 11 inches by 15 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be if the area of the mounted picture is 285 square inches?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A picture 11 inches by 15 inches is to be mounted on a piece of mat-board so that there is an even amount of mat all around the picture. How wide will the border be if the area of the mounted picture is 285 square inches?
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Let the width of the border = x
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From the reading of the problem we can write an equation like this:
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Mat width * Mat length = 285 sq/in
(2x+11) * (2x+15) = 285
FOIL
4x^2 + 30x + 22x + 165 = 285
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4x^2 + 52x + 165 - 285 = 0
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4x^2 + 52x - 120 = 0
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Simplify, divide by 4:
x^2 + 13x - 30 = 0
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A quadratic equation that we can factor:
(x + 15)(x - 2) = 0
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Obviously only x = 2 inches can be the solution:
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Check solution by finding the area:
(11+4) * (15+4) =
15 * 19 = 285
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Did this make sense?