Final answer:
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.