A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 4 inches wide on each side, the total area would have been (M + 90) square inches. What is the perimeter of the photograph, in inches? Choose the correct choice from the following
A) 10  B) 20  C) 30  D) 40  E) 50
Let x and y be the width and length of the photograph.   (x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M   (x+8)(y+8)=M and so (2) xy + 8x + 8y + 64 = M+90   Let's subtract equation (1) from equation (2).   6x + 6y + 60 = 90   2x + 2y = 10, which is the perimeter of the photograph.   The answer is 10.
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A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 4 inches wide on each side, the total area would have been (M + 90) square inches. What is the perimeter of the photograph, in inches?