SOLUTION: A 16- inch by 20-inch mounting board is used to mount a photogrpah. How wide a uniform border is needed if the photograph occupies 3/5 of the area of the mounting board?
I want
Question 667779: A 16- inch by 20-inch mounting board is used to mount a photogrpah. How wide a uniform border is needed if the photograph occupies 3/5 of the area of the mounting board?
I want desperately to understand word problems, but I'm so stuck. Please help! Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A 16- inch by 20-inch mounting board is used to mount a photograph.
How wide a uniform border is needed if the photograph occupies 3/5 of the area of the mounting board?
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Find the area of the mounting board: 16 * 20 = 320 sq/in
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Find the area of of photo: * 320 = 192 sq/in
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Let x = the width of the border around the photo
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The border subtracts 2x from the mounting board dimensions, leaving the area of the photo:
therefore
(16-2x)*(20-2x) = 192
FOIL
320 - 32x - 40x + 4x^2 = 192
Arrange as a quadratic equation
4x^2 - 72x + 320 - 192 = 0
4x^2 - 72x + 128 = 0
Simplify, divide by 4
x^2 - 18x + 32 = 0
You can use the quadratic formula, but this will factor to
(x-2)(x-16) = 0
two solutions, but only one will be reasonable
x = 2 inches is the width of the border
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:
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See if this checks out: (16-4)*(20-4) = 192, the area of the photo
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Did this help you understand this problem, any questions? C
