SOLUTION: A picture frame holds a 4in by 6 in photo. The frame adds a border x inches wide around three sides of the photo. On the fourth side the frame forms a border that is 3x-0.5 in wide

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Question 859616: A picture frame holds a 4in by 6 in photo. The frame adds a border x inches wide around three sides of the photo. On the fourth side the frame forms a border that is 3x-0.5 in wide. The combined area of photo and frame is 80.5 inē. Write a quadratic equation for the combined area. Then use the formula to find x.......this is my daughters homework and I cant figure it out...please help

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A picture frame holds a 4in by 6 in photo.
The frame adds a border x inches wide around three sides of the photo.
On the fourth side the frame forms a border that is 3x-0.5 in wide.
The combined area of photo and frame is 80.5 inē.
Write a quadratic equation for the combined area.
:
The area of the top portion which does not include the bottom border area\
FOIL
(2x+4)(x+6) = 2x^2 + 12x + 4x + 24 = 2x^2 + 16x + 24
The area of the bottom border
(2x+4)(3x-.5) = 6x^2 - x + 12x - 2 = 6x^2 + 11x - 2
Total area = 80.5
(2x^2 + 16x + 24) + (6x^2 + 11x - 2) = 80.5
Combine like terms
2x^2 + 6x^2 + 16x + 11x + 24 - 2 - 80.5 = 0
f(x) = 8x^2 + 27x - 58.5, the quadratic equation of the combined area
:
Then use the formula to find x.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=8, b=27, c=-58.5
x+=+%28-27+%2B-+sqrt%2827%5E2-4%2A8%2A-58.5+%29%29%2F%282%2A8%29+
You can do the math here, I came up with reasonable answer of x=1.5"