SOLUTION: A 3 inch border is added around a photograph of unknown dimensions. If the length of the photo is one inch less than twice the width of the photo, and the area of the photo and bor

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Question 285775: A 3 inch border is added around a photograph of unknown dimensions. If the length of the photo is one inch less than twice the width of the photo, and the area of the photo and border together is 130 square inches, what is the area of the photo?
A. 15 in2 B. 28 in2 C. 45 in2 D. 66 in2 E. None of these.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the width of the photo x in, then
the length is 2x+-+1 in.
the area of the photo is
x%2A%282x+-+1%29+=+2x%5E2+-+x
The area of the photo plus border is
%28x+%2B+6%29%2A%282x+-+1+%2B+6%29
%28x+%2B+6%29%2A%282x+%2B+5%29
2x%5E2+%2B+17x+%2B+30
The area of photo plus border is 130 in2
2x%5E2+%2B+17x+%2B+30+=+130
2x%5E2+%2B+17x+-+100+=+0
using quadratic equation:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+2
b+=+17
c+=+-100
x+=+%28-17+%2B-+sqrt%28+17%5E2-4%2A2%2A%28-100%29+%29%29%2F%282%2A2%29+
x+=+%28-17+%2B-+sqrt%28+289+%2B+800+%29%29%2F4+
x+=+%28-17+%2B-+33%29%2F4+
x+=+%28-17+%2B+33%29%2F4
x+=+16%2F4
x+=+4
2x+-+1+=+2%2A4+-+1
2x+-+1+=+7
Area of photo = 4%2A7
4%2A7+=+28 in2
The answer is (B)