# How much pure acid should be mixed with 2 gallons of a 50% acid solution in order to get an 80% acid solution?

May 2, 2017

You should add 3 gal of pure acid to 2 gal of 50 % acid.

#### Explanation:

You have

$\text{100 % acid + 50% acid → 80 % acid}$

You can use the dilution formulas

${c}_{1} {V}_{1} + {c}_{2} {V}_{2} = {c}_{3} {V}_{3}$

Let the volume of pure acid be $x$ gal. Then

100 color(red)(cancel(color(black)(%))) × x color(red)(cancel(color(black)("gal"))) + 50 color(red)(cancel(color(black)(%))) × 2 color(red)(cancel(color(black)("gal"))) = 80 color(red)(cancel(color(black)(%))) × (x + 2) color(red)(cancel(color(black)("gal")))

$100 x + 100 = 80 x + 160$

$20 x = 60$

$x = 3$

∴ You add 3 gal of 100 % acid to 2 gal of 50 % acid.