Originally Posted by

**TheEmptySet** You are correct that the above post is wrong, I had a serious brain cramp!

$\displaystyle \displaystyle \alpha=\frac{a(M+N)}{M}, \text{ and } \beta=\frac{b(M+N)}{N}$

Where $\displaystyle a$ is the intial amount of A

Where $\displaystyle b$ is the intial amount of B

M is the proportion of A and N is the proportion of B

$\displaystyle \displaystyle \alpha=\frac{a(M+N)}{M}=\frac{40(2+1)}{2} $

$\displaystyle \displaystyle \beta=\frac{b(M+N)}{N}=\frac{50(2+1)}{1} $

Now we get

$\displaystyle \displaystyle \left( \frac{40(2+1)}{2}-X\right) \left( \frac{50(2+1)-X}{1}\right)=\frac{1}{2}(120-2X)(150-X)$

Again sorry for the brain cramp!