Question

Faith mixes 14 liters of 12% acid solution with a 30% acid solution to make a 18% acid solution

Answer 1

Suppose Faith mixes the 14 L of 12% solution with
`x` L of the 30% solution. Then the new solution, with a concentration of 18% acid, has a total volume of
`14+x` 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

`0.12\cdot14+0.3x=0.18(14+x)`

Solve for
`x`:

`1.68+0.3x=2.52+0.18x`

`0.12x=0.84`

`x=7`

So Faith must use 7 L of the 30% solution to end up with the concentration she wants.