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