Answer
The quantity of the $60\%$ acid solution is $=7.5\;L$
The quantity of the $100\%$ acid solution is $=4.5\;L$
Work Step by Step
Let the quantity of the $60\%$ acid solution is $=x$
Let the quantity of the $100\%$ acid solution is $=y$
Total solution $x+y=12$......(1)
Quantity of the acid
$60\%$ of $x+$ $100\%$ of $y=75\%$ of $12\;L$
Rewrite as an equation.
$0.60x+y=9$......(2)
Subtract equation (2) from equation (1).
$x+y-(0.60x+y)=12-9$
Simplify.
$x+y-0.60x-y=3$
$0.40x=3$
$x=\frac{3}{0.40}$
$x=7.5\;L$
Substitute the value of $x$ into equation (1).
$7.5+y=12$
Subtract $7.5$ from both sides.
$7.5+y-7.5=12-7.5$
Simplify.
$y=4.5\;L$
