# Roman mixes 12 litres of 8% acid solution with a 20% acid solution, which results in a 16% acid solution. How do you find the number of litres of 20% acid solution in the new mixture?

Dec 31, 2016

The volume of 20 % acid is 24 L.

#### Explanation:

We can use the "volume × concentration" formula to work out the answer.

$\text{Volume of 8 % acid + volume of 20 % acid = volume of 16 % acid}$

Let $x$ be the volume of 20 % acid.

Then $\left(12 + x\right) \textcolor{w h i t e}{l} \text{L}$ is the new volume of the 16 % acid.

We can write

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

12 color(red)(cancel(color(black)("L"))) × 8 color(red)(cancel(color(black)(%))) + x color(red)(cancel(color(black)("L"))) × 20 color(red)(cancel(color(black)(%))) = (12 +x) color(red)(cancel(color(black)("L"))) × 16 color(red)(cancel(color(black)(%)))

$96 + 20 x = 192 + 16 x$

$4 x = \text{192 - 96} = 96$

$x = \frac{96}{4} = 24$

∴ The volume of 20 % acid is 24 L.