If $x$ and $y$ are positive integers for which $3x + 2y + xy = 115$, then what is $x + y$?
3x + 2y + xy = 115
3x + xy = 115 - 2y
x ( 3 + y) = 115 - 2y
x = (115 - 2y) / ( 3 + y)
Note that when y = 8
x = (115 - 2*8) / ( 3 + 8) = 99 / 11 = 9
So
x = 9 and y = 8
x + y = 17
+501 
