A specialized alloy is created by mixing two metals, $X$ and $Y$. Alloy $A$ has a ratio of $X:Y = 2:3$, and Alloy $B$ has a ratio of $X:Y = 4:1$. If you mix these two alloys to create a final mixture with a ratio of $X:Y = 1:1$, what must be the ratio of the weight of Alloy $A$ to the weight of Alloy $B$?