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 $x:y:z=4:1:1$.