Suppose Faith mixes the 14 L of 12% solution with [tex]x[/tex] L of the 30% solution. Then the new solution, with a concentration of 18% acid, has a total volume of [tex]14+x[/tex] L.
For each liter used of the 12% solution, 0.12 L of acid is contributed; for each liter of the 30% solution used, 0.3 L of acid is contributed. In the new solution, each liter contributes 0.18 L of acid. So the amount of acid in the mixture satisfies
[tex]0.12\cdot14+0.3x=0.18(14+x)[/tex]
Solve for [tex]x[/tex]:
[tex]1.68+0.3x=2.52+0.18x[/tex]
[tex]0.12x=0.84[/tex]
[tex]x=7[/tex]
So Faith must use 7 L of the 30% solution to end up with the concentration she wants.
