Question

Jerry is experimenting with chemicals in the laboratory. He mixes a solution that is 10% acid with a solution that is 30% acid. How much of the 10% acid solution will be needed to make 40 liters of a solution that is 25% acid?

Answer 1

The formula:
$\hbox{volume percent} = \frac{\hbox{volume of solute}}{\hbox{volume of solution}} \cdot 100\%$

Data:
$\hbox{volume percent}_1 =10\% \\ \hbox{volume of solution}_1= x \\ \hbox{volume of solute}_1 = 10\% x=0.1x \\ \\ \hbox{volume percent}_2 =30\% \\ \hbox{volume of solution}_2= y \\ \hbox{volume of solute}_2 = 30\% y=0.3x \\ \\ \hbox{volume percent}_3 =25\% \\ \hbox{volume of solution}_3= 40 \ l \\ \hbox{volume of solute}_1 = 25\% \cdot 40 \ l =10 \ l$

You need to make 40 l of a solution with 10 l of solute.
$\hbox{volume of solute}_1+ \hbox{volume of solute}_2 = 10 \ l \\ \hbox{volume of solution}_1 + \hbox{volume of solution}_2= 40 \ l$

Therefore:
$\left \{ {{0.1x+0.3y=10} \atop {x+y=40}} \right. \\ \\ \left \{ {{x+3y=100} \atop {-x-y=-40}} \right. \\ x-x+3y-y=100-40 \\ 2y=60 \\ y=30 \\ -x-30=-40 \\ -x=-10 \\ x=10 \\ \left \{ {{x=10} \atop {y=30}} \right.$

You will need 10 liters of the 10% acid.