11.5 liters of the 26% alcohol solution and 12.5 liters of the 11% alcohol solution should be mixed to make 24 liters of a solution that is 21% alcohol.
To create a 24-liter solution with 21% alcohol, a mixture of two antifreeze solutions—one with 26% alcohol and another with 11% alcohol—can be combined. Let x represent the volume (in liters) of the 26% alcohol solution, and y represent the volume of the 11% alcohol solution. The total volume constraint is x+y=24 liters.
The concentration constraint is expressed as 0.26x+0.11y=0.21×24, where the left side represents the total amount of alcohol in the mixture, and the right side represents the desired concentration of 21%.
Solving these simultaneous equations gives x=11.5 liters and y=12.5 liters. Therefore, mixing 11.5 liters of the 26% alcohol solution with 12.5 liters of the 11% alcohol solution will result in a total volume of 24 liters with the desired alcohol concentration of 21%.