Is it possible to find the ratio of isotopes only given the mean mass number? Three isotopes of an element have mass numbers $(M)$, $(M+1)$ and $(M+2)$. If the mean mass number is $(M+0.5)$, then the ratio of the amounts of the three isotopes is?


Let amount of $(M)$, $(M+1)$, and $(M+2)$ be $x$, $y$ and $z$ respectively.
$$\frac{(M)x + (M + 1)y + (M + 2)z}{x + y + z} = (M + 0.5)$$

After further simplification, I got $x-y=3z$.

I don't know how to proceed further. Can someone give me a hint, or reassure me that this question can't be solved with the given data?

The answer is given as $x:y:z=4:1:1$.
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.