The cost of picture framing depends on the outer perimeter of the frame if a 15 inch by 15 inch picture frame cost $35 more than a 10 inch by 10 inch picture frame what is the cost of framing in dollars per inch?

Let c be the cost of a 10" by 10" frame.  Then 

2(15 in)+ 2(15 in) = c+$35, so 60 in = c + $35

c = 4(10)= $40 for the 10 by 10 inch frame; ($40+$35), or $75, for the 15 by 15 inch frame.

cost per inch is $75/60 in, or $1.25/inch.  Same as $40/ 40 inches, or $1/inch.  Can't have 2 different answers!

Let's try again.  This time, let C represent the cost of the frame material in dollars per inch.

The 10 by 10 frame would cost (40 inches)C.

The 15 by 15 frame would cost (60 inches)C

and (60 inches)C = (40 inches)C + $35

Then 60C = 40C + $35
so that    20C = $35, and C = cost per inch = $35/20 inches = $1.75/inch (answer)