Question

In the following exercises, translate to a system of equations and solve.

A scientist needs 120 liters of a 20% acid solution for an experiment. The lab has available a 25% and a 10% solution. How many liters of the 25% and how many liters of the 10% solutions should the scientist mix to make the 20% solution?

Short answer

The number of 25% solution is 80 ml and number of 10% solution is 40 ml.

Step-by-step solution

Step 1. Given Information   

The given data is that scientist needs 120 liters of a 20% acid solution for an experiment. The lab has available a 25% and a 10% solution.

Step 2. Explanation  

Let number of units of 25% solution be x and number of units of 10% solution be y.

The number of units of 20% solution is 120 ml.

Thus, the total units of solution can be expressed as $x+y=120--\left(1\right)$

The amount of 20% solution is$120\times 0.2=24$

And the total amount of solution can be expressed as$0.25x+0.1y=24--\left(2\right)$

Step 3. Calculation   

Multiply equation (1) with number $0.25$and write the revised equation.

$$\begin{gathered} 0.25(x+y)=0.25\left(120\right) \\ 0.25x+0.25y=30--\left(3\right) \end{gathered}$$

Solve the equation (3) and (2) by subtracting equation (2) from equation (3).

$$\begin{gathered} 0.25x+0.25y-0.25x-0.1y=30-24 \\ 0.15y=6 \\ y=40 \end{gathered}$$

Substitute the value of y in equation (1) to find the value of x.

$$\begin{gathered} x+y=120 \\ x=120-40 \\ x=80 \end{gathered}$$