# What volumes of a 2 % solution and a 6 % solution must I mix to get 300 mL of a 5 % solution?

Jul 4, 2017

You must mix ${\text{75 cm}}^{3}$ of the 2% solution and ${\text{225 cm}}^{3}$ of the 6 % solution.

#### Explanation:

We can use a modification of the dilution formula to solve this problem:

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} {V}_{1} {c}_{1} + {V}_{2} {c}_{2} = {V}_{3} {c}_{3} \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

Let $x$ = the volume of 2 %.
Then $300 - x$ = the volume of 6 %.

Then

x × 2color(red)(cancel(color(black)(%))) + (300-x) × 6color(red)(cancel(color(black)(%))) = 300 × 5color(red)(cancel(color(black)(%)))

$2 x + 1800 - 6 x = 1500$

$4 x = 300$

$x = \frac{300}{4} = 75$

∴ You must use ${\text{75 cm}}^{3}$ of 2% and ${\text{225 cm}}^{3}$ of 6 %.

Check:

75 × 0.02 + 225 × 0.06 = 300 × 0.05

$1.5 + 13.5 = 15$

$15 = 15$

It checks!