Is it possible to find the ratio of isotopes only given the mean mass number?
You have two equations and 3 unknowns, so you can't solve it with just that. Say a, b, c are the fractions (as a decimal) of each isotope...

$$ a(x) + b(x+1) + c(x+2) = (x+\frac{1}{2}) $$

$$a + b + c = 1 $$

The 4:1:1 solution works. Another that works is 3:0:1. Another is 7:4:1. There are infinitely many solutions.