.
Assuming the width of the frame uniform, let x be the frame width.
Then the dimensions of the painting itself are 32-2x and 29-2x inches.
The area equation for the painting is
(32-2x)*(29-2x) = 550.
Simplify and solve for x.
For many other similar solved problems see the lesson
- Problems on the area and the dimensions of a rectangle surrounded by a strip
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements".