Question

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

Joy is preparing 15 liters of a 25% saline solution. She only has 40% and 10% solution in her lab. How many liters of the 40% and how many liters of the 10% should she mix to make the 25% solution?

Short answer

The number of 40% solution is $7.5$litres and number of 10% solution is $7.5$litres.

Step-by-step solution

Step 1. Given Information 

The given data is that Joy is preparing 15 liters of a 25% saline solution. She only has 40% and 10% solution in her lab.

Step 2. Explanation    

Let number of units of 40% solution be x and number of units of 10% solution be y.

The number of units of 25% solution is 15 liters.

Thus, the total units of solution can be expressed as $x+y=15--\left(1\right)$

The amount of 25% solution is $15\times 0.25=3.75$

And the total amount of solution can be expressed as$0.4x+0.1y=3.75--\left(2\right)$

Step 3. Calculation  

Multiply equation (1) with number $0.4$and write the revised equation.

$$\begin{gathered} 0.4(x+y)=0.4\left(15\right) \\ 0.4x+0.4y=6--\left(3\right) \end{gathered}$$

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

$$\begin{gathered} 0.4x+0.1y-0.4x-0.4y=3.75-6 \\ -0.3y=-2.25 \\ y=7.5 \end{gathered}$$

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

$$\begin{gathered} x+y=15 \\ x=15-7.5 \\ x=7.5 \end{gathered}$$