(In reply to Solution
Nice start, Broll, and thanks for citing my method.
However, there is no reason to assume that GO/IN is a fraction that has been reduced to lowest terms.
kx = 999 = 27*37, so IN could be 27 or 37. But IN could also be a multiple of 27 (ie, 54 or 81) or a multiple of 37 (ie, 74).
This turns out not to be the case, but a full analytical solution needs to deal with that possibility.