SOLUTION: Hi. I've tried this problem multiple times now, but I'm still not getting an answer that would make sense. Can anyone please help me? The problem is: The outside of a picture fr

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hi. I've tried this problem multiple times now, but I'm still not getting an answer that would make sense. Can anyone please help me? The problem is: The outside of a picture fr      Log On


   

Question 1074695: Hi. I've tried this problem multiple times now, but I'm still not getting an answer that would make sense. Can anyone please help me?
The problem is:
The outside of a picture frame measures 12in by 18in. 72in^2 of the picture shows. Find the thickness of the frame.
Any ideas? So far I have gotten ridiculous solutions like 17, 12 and 3.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Area of total outside dimensions,12%2A18%2Ainch%5E2

w, uniform WIDTH of the frame around the picture
%2812-2w%29%2818-2w%29, the area without the border, equal to the picture area.

highlight_green%28%2812-2w%29%2818-2w%29=72%29
Simplify and solve for w.

-
2%2A2%2A%286-w%29%289-w%29=72
%286-w%29%289-w%29=18
54-15w%2Bw%5E2=18
w%5E2-15w%2B54-18=0
w%5E2-15w%2B36=0
%28w-3%29%28w-12%29=0

You KNOW that w of 12 will NOT work.
highlight%28w=3%29

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
The size of the picture is 12 x 6 inches.

All you need to do is to find two factors of 72 that differ in 6.

So, the thickness of the frame is 3 inches.

This problem is for MENTAL solution.