Question

A mixture of 12% alcohol is to be made from 15% alcohol and 9% alcohol. How much of each solution should be used to obtain 30 liters of the 12% alcohol solution?

Answer 1

To mix two alcohol solutions to achieve a 12% alcohol mixture totaling 30 liters, we use a system of two equations representing the total volume and the alcohol concentration to find the volumes of 15% and 9% alcohol solutions required.

Step-by-step explanation:

To solve the problem of mixing two alcohol solutions to obtain a desired percentage, we can set up a system of equations based on the total volume and concentration of alcohol.

Let's denote x as the volume of the 15% alcohol solution and y as the volume of the 9% alcohol solution required. The total volume needed is 30 liters, so we have:

x + y = 30

Next, we need to set up an equation based on the concentration of alcohol:

0.15x + 0.09y = 0.12 * 30

Solving these equations simultaneously gives us the exact volumes of each solution needed to create the 30 liters of 12% alcohol solution.

By substitution or using the elimination method, we find the values for x and y, which will determine how much of each alcohol solution is needed.