SOLUTION: An 8 in. by 10 in. picture is matted and placed in a frame that will display a total of 143 in. of area. The mat provides a uniform border surrounding the picture. Determine the wi

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Question 885687: An 8 in. by 10 in. picture is matted and placed in a frame that will display a total of 143 in. of area. The mat provides a uniform border surrounding the picture. Determine the width of the mat.
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39613) (Show Source):
You can put this solution on YOUR website!
"Mat", "matted", "matting". This is what surrounds the picture. Description needed to be checked carefully to understand this.

The picture is only square inches. Let x = width of uniform border for the matting around the picture. The 143 square inch area is .

Form and solve this equation for x:

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The algebra for that quadratic equation should not be complicated. Tell if you need help.

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
The area of the picture is in2
The total area is in2
The area of the mat is in2
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Let = the width of the mat
is added to each dimension of the picture to
make the area of picture + mat

Complete the square

Take the square root of both sides

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The width of the mat is 3 in
check:
Mat + picture = 143

OK