Chapter 6, Problem 15CT

To determine

To find the quantity of each solution the chemist mix to get 200 L of a 42% insecticide.

Answer to Problem 15CT

80 liters of 30% solution and 120 liters of 50% solution is needed.

Explanation of Solution

Given:

Chemist has one solution containing 50% insecticide and another solution containing 30% insecticide.

Calculation:

Let x liters of 30% insecticide solution and y liters of 50% insecticide solution be mixed to get 200 L of a 42% insecticide. Then,

  $\begin{array}{l}x+y=200\left[\text{Total}\text{quantity}\right]\\ \Rightarrow y=200-x\to \left(1\right)\\ \&\\ \frac{30}{100}x+\frac{50}{100}y=\frac{42}{100}\left(x+y\right)\left[\text{Total}\text{insecticide}\right]\\ \Rightarrow 30x+50y=42\left(200\right)\\ \Rightarrow 30x+50\left(200-x\right)=8400\left[\text{Using}\text{equation}\left(\text{1}\right)\right]\\ \Rightarrow 30x+10000-50x=8400\\ \Rightarrow -20x=-1600\\ \Rightarrow x=80\end{array}$

Now put $x=80$ in equation (1), we get

  $\begin{array}{l}y=200-80\\ \Rightarrow y=120\end{array}$

Therefore 80 liters of 30% solution and 120 liters of 50% solution is needed.