Question

Two casks $A$ and $B$ were filled with two kinds of sherry, mixed in the cask $A$ in the ratio of $2:7$, and in the cask $B$ in the ratio of $1:5$. What quantity must be taken from each to form a mixture which shall consist of $2$ gallons of one kind and $9$ gallons of the other?

Answer 1

Let $x$ gallons were taken from cask $A$ and $y$ gallons from cask $B$

Then for $x$ gallons from cask $A$ we have $\frac{2}{9}x$ gallons of first kind and for $y$ gallons from cask $B$ we have $\frac{1}{6}y$ gallons of first kind.

Also $x+y=11$

And we have $2$ gallons of first kind. So,

$\frac{2}{9}x+\frac{1}{6}y=2$

$x+y=11$

multiplying the second equation by $\frac{1}{6}$and subtracting from first

$\frac{2}{9}x-\frac{1}{6}x=2-\frac{11}{6}$

$x=3$

So,

$3+y=11$

$y=8$