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 173624This question is from textbook Introductory Algebra
: 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? This question is from textbook Introductory Algebra

Answer by nerdybill(7384) (Show Source):
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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?
.
Let x = width of border
.
If we have the border, the picture's area is:
(11+2x)(15+2x) = 285
(11+2x)(15+2x) = 285
165 + 22x + 30x + 4x^2 = 285
4x^2 + 52x + 165 = 285
4x^2 + 52x - 120 = 0
x^2 + 13x - 30 = 0
(x+15)(x-2) = 0
.
x = {-15, 2}
We can toss out the negative solution leaving us with:
x = 2 inches (width of border)