# Question #56180

Jun 17, 2016

${V}_{60} = 216.6 \text{ml}$

${V}_{15} = 433.3 \text{ml}$

#### Explanation:

You use the idea that

$\text{concentration=amount of substance/volume of solution}$

In symbols:

$c = \frac{n}{v}$

This means that

$n = c \times v$

In questions like this the total amount of substance does not change so we can write:

$\left(60 \times {V}_{60}\right) + \left(15 \times {V}_{15}\right) = 30 \times 650 \text{ } \textcolor{red}{\left(1\right)}$

We also know that the total volume is $650 \text{ml}$ so we can also write:

${V}_{60} + {V}_{15} = 650 \text{ } \textcolor{red}{\left(2\right)}$

So we have set up two simultaneous equations. There are two equations and two unknowns so they can be solved easily.

From $\textcolor{red}{\left(2\right)}$ we can rearrange:

${V}_{60} = \left(650 - {V}_{15}\right)$

We now substitute this expression for ${V}_{60}$ into $\textcolor{red}{\left(1\right)} \Rightarrow$

$60 \left(650 - {V}_{15}\right) + 15 {V}_{15} = 19500$

$\therefore 39000 - 60 {V}_{15} + 15 {V}_{15} = 19500$

$\therefore 39000 - 45 {V}_{15} = 19500$

$\therefore 45 {V}_{15} = 39000 - 19500 = 19500$

$\therefore {V}_{15} = \frac{19500}{45} = 433.3 \text{ml}$

From $\textcolor{red}{\left(2\right)}$ we know that:

${V}_{60} + {V}_{15} = 650$

$\therefore {V}_{60} = 650 - {V}_{15}$

$\therefore {V}_{60} = 650 - 433.3 = 216.6 \text{ml}$