# A chemist has one solution containing 30% insecticide and another solution containing 50% insecticide. How much of each solution should the chemist mix to get 200 L of a 42% insecticide?

Apr 1, 2016

He or she should use $79.6 \text{L}$ of the 30% solution and $120.4 \text{L}$ of the 50% solution.

#### Explanation:

Amount of substance = concentration x volume.

Let $x$ = the volume of the 30% solution.

Let $y$ = the volume of the 50% solution.

Because the total amount of insecticide does not change
we can set up 2 simultaneous equations:

$\left(200 \times 42\right) = \left(30 \times x\right) + \left(50 \times y\right) \text{ } \textcolor{red}{\left(1\right)}$

$x + y = 200 \text{ } \textcolor{red}{\left(2\right)}$

$\textcolor{red}{\left(1\right)}$ becomes:

$8400 = 30 x + 50 y$

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

$x = 200 - y$

Substitute this for $x$ into $\textcolor{red}{\left(1\right)} \Rightarrow$

$8400 = 30 \left(200 - y\right) + 50 y$

$8400 = 6000 - 30 y + 50 y$

$2408 = 20 y$

$y = \frac{2408}{20} = 120.4 \text{L}$

Substitute this back into $\textcolor{red}{\left(2\right)} \Rightarrow$

$x = 200 - 120.4 = 79.6 \text{L}$