The formula:
[tex]\hbox{volume percent} = \frac{\hbox{volume of solute}}{\hbox{volume of solution}} \cdot 100\%[/tex]
Data:
[tex]\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 \\[/tex]
You need to make 40 l of a solution with 10 l of solute.
[tex]\hbox{volume of solute}_1+ \hbox{volume of solute}_2 = 10 \ l \\
\hbox{volume of solution}_1 + \hbox{volume of solution}_2= 40 \ l[/tex]
Therefore:
[tex] \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. [/tex]
You will need 10 liters of the 10% acid.
