Question

A rectangular photograph is mounted on a poster and has a two inch border on each side. The poster itself is mounted on a frame whose sides are the same length as the sides of the poster. The frame cost $2 per inch and the cost of the frame was $160. If the area of the photograph is 231 inches squared. What are the dimensions of the frame?

Answer 1

Let's define variables:
w: width of the photograph
l: length of the photograph
The cost of the box is:
2 * (2 * (w + 2)) + 2 * (2 * (l + 2)) = 160
The area is:
(w + 2) * (l + 2) = 231
Solving the system of equations we have:
w = 5 inches
l = 31 inches
Then, the dimensions of the frame are:
w + 2 = 7 inches
l + 2 = 33 inches
Answer:
the dimensions of the frame are:
7 inches * 33 inches