If x and y are positive integers for which 3x + 2y + xy = 117, then what is x + y?
3x + xy + 2y = 117
x(3+y) + 2y = 117
x(3+y) + 2y + 6 = 123
x(3+y) + 2(y+3) = 123
(x+2)(y+3) = 123
123 = 41 x 3
x + 2 = 3
y + 3 = 41
x = 1, y = 38
x + y = 39.
