Final answer:
To produce a 23% acid solution, 24 liters of a 24% acid solution should be mixed with 3 liters of a 15% acid solution. The problem was solved using a mixture equation, taking into account the total amount of pure acid before and after the mixing process.
Step-by-step explanation:
To determine how many liters of a 24% acid solution should be mixed with 3 liters of a 15% acid solution to produce a 23% solution, we can set up a simple mixture problem. We will leverage the concept that the total amount of pure acid in the solution before mixing should be equal to the total amount of pure acid in the final solution.
Let x represent the number of liters of the 24% acid solution that needs to be mixed. The amount of acid in the 24% solution is 0.24x liters, and the amount of acid in the 3 liters of 15% solution is 0.15(3) liters. Since the final solution must be 23% acid, the equation representing the mixture is:
0.24x + 0.15(3) = 0.23(x + 3)
Solve this equation for x to find the volume of 24% solution needed:
0.24x + 0.45 = 0.23x + 0.69
0.01x = 0.24
x = 24 liters
Therefore, 24 liters of a 24% acid solution should be mixed with 3 liters of a 15% acid solution.