91Ó°ÊÓ

A pharmacist needs 20 liters of a 2% saline solution. He has a 1% and a 5% solution available. How many liters of the 1% and how many liters of the 5% solutions should he mix to make the 2% solution?

We are looking for how much of each solution he needs.

Let x=number of liters of 1% solution.

y=number of liters of 5% solution

A table will help us organize the data.

$$\begin{gathered} x+y=20………………\mathrm{Equation}1 \\ 0.01x+0.05y=0.4………………\mathrm{Equation}2 \end{gathered}$$

Now we solve the system of equations.

$$\begin{gathered} 0.05\left(x+y\right)=20×0.05 \\ 0.05x+0.05y=1………………\mathrm{Equation}3 \end{gathered}$$

Subtract Equation 3 and Equation 2.

$$\begin{gathered} 0.05x+0.05y-\left(0.01x+0.05y\right)=1-0.4 \\ 0.05x+0.05y-0.01x-0.05y=0.6 \\ 0.04x=0.6 \\ \mathrm{Divide}\mathrm{by}0.04\mathrm{on}\mathrm{both}\mathrm{side} \\ \frac{0.04}{0.04}\mathrm{x}=\frac{0.6}{0.04} \\ \mathrm{x}=15 \end{gathered}$$

$$\begin{gathered} x+y=20 \\ 15+y=20 \\ \mathrm{Subtract}15\mathrm{on}\mathrm{both}\mathrm{side} \\ 15+y-15=20-15 \\ y=5 \end{gathered}$$

He should mix 15 litre solution of 1% and 5 liter solution of 5% to make the 2% saline solution.