Question

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

A 90% antifreeze solution is to be mixed with a 75% antifreeze solution to get 360 liters of a 85% solution. How many liters of the 90% and how many liters of the 75% solutions will be used?

Short answer

The number of 90% solution is 240 litres and number of 75% solution is 120 litres.

Step-by-step solution

Step 1. Given Information 

The given data is that a 90% antifreeze solution is to be mixed with a 75% antifreeze solution to get 360 liters of a 85% solution.

Step 2. Explanation    

Let number of units of 90% solution be x and number of units of 75% solution be y.

The number of units of 85% solution is 360 litres.

Thus, the total units of solution can be expressed as $x+y=360--\left(1\right)$

The amount of 85% solution is$360\times 0.85=306$

And the total amount of solution can be expressed as$0.9x+0.75y=306--\left(2\right)$

Step 3. Calculation 

Multiply equation (1) with number $0.9$and write the revised equation.

$$\begin{gathered} 0.9(x+y)=0.9\left(360\right) \\ 0.9x+0.9y=324--\left(3\right) \end{gathered}$$

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

$$\begin{gathered} 0.9x+0.9y-0.9x-0.75y=324-306 \\ 0.15y=18 \\ y=120 \end{gathered}$$

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

$$\begin{gathered} x+y=360 \\ y=360-120 \\ y=240 \end{gathered}$$