SOLUTION: A picture 19 inches by 24 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 300980: A picture 19 inches by 24 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 border is 188 square inches?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A picture 19 inches by 24 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 border is 188 square inches?
:
Find the area of the picture
A = 19 * 24
A = 456 sq/in
:
Let x = width of the border
:
The overall dimensions including the border: (2x + 19) by (2x + 24)
:
Overall area - picture area = 188
(2x+19)*(2x+24) - 456 = 188
FOIL
4x^2 + 48x + 38x + 456 - 456 = 188
:
4x^2 + 86x - 188 = 0
:
Simplify, divide by 2
2x^2 + 43x - 94 = 0
Factor
(2x + 47)(x - 2) = 0
the positive solution
x = 2 in is the width
:
:
Check solution
overall dimensions 23 by 28
(23*28) - 456 =
644 - 456 = 188; confirms our solution of x=2