If we add x liters of the pure acid, we must have 90-x liters of 10% acid solution.
The equation that represents the situation:
[tex]\begin{gathered} x+0.1(90-x)=.40(90) \\ x+9-0.1x=36 \end{gathered}[/tex]Solve for x to determine the liters of pure acid:
[tex]\begin{gathered} 0.9x=36-9 \\ 0.9x=27 \\ x=\frac{27}{0.9} \\ x=30 \end{gathered}[/tex]30 liters of pure acid need to be used to make the solution.
Then, 90-x would be the amount of the 10% acid solution:
[tex]90-30=60[/tex]60 Liters of 10% acid solution is needed to make the solution.
