Question 1170832
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This problem can be solved in a few seconds informally, with just a bit of mental arithmetic.<br>
One response you have received presumably used an automatic problem solver; but something is wrong somewhere in the calculations, and the solution is irrational and therefore only approximate.<br>
The other response fails to see the solution, after setting up the problem correctly.<br>
But the dimensions of the picture are "nice' numbers; here is the quick and easy informal solution....<br>
The difference between the length and width of the frame (including picture) is 4 inches; since the frame around the picture is of uniform width, the difference between the length and width of the picture is 4 inches.<br>
So to solve the problem, we only need to find two numbers with a difference of 4 and a product of 192.  Of course you could solve <i>THAT</i> problem algebraically; but some quick mental arithmetic finds the numbers to be 12 and 16.<br>
So the picture is 12 inches by 16 inches; since the picture with frame is 28 inches by 32 inches, the width of the frame is 8 inches.<br>