Again I believe this is a number theoretic question.I have never had a formal course in cryptography, but I know a little bit of number theory.

I think this question is essentially asking, find the largest number of x's such that is a bijection. Since .

This means there are 49 values of x which will map to a unique (9x mod 49).

Since we have already added 27 letters, we can add 22(=49-27) more letters to the alphabet without any further changes to our encoding procedure.

Again, feel free to point my mistakes. Since I am not entirely sure whether the utility of the affine enciphering stems from its bijective nature. It looks like common sense, but I am not sure