Is it possible to determine the composition of a gas mixture from the effusion of a gas through a pinhole?
Go on! You are nearly at the end. If you square your equation, and replace $y$ by $1-x$, you obtain: $$(24/20)^2 = \frac{32·x + 44(1-x)}{28}$$ 
You finally obtain: $x = 1/3$ and $y = 2/3$.