Final answer:
To prepare 50 liters of a 25% acid solution, mix 40 liters of a 20% solution with 10 liters of a 45% solution by solving a system of linear equations.
Step-by-step explanation:
To determine how many liters of a 20% acid solution and a 45% acid solution are needed to produce 50 liters of a 25% acid solution, we use the concept of mixtures in algebra. Let x be the amount of 20% solution and y be the amount of 45% solution needed.
First, we establish two equations based on the given information:
- The total volume of the solutions must add up to 50 liters:
x + y = 50 - The total amount of acid in the mixed solution must be 25% of 50 liters:
0.20x + 0.45y = 0.25(50)
Solving these two equations simultaneously, we can find the values of x and y.
Step 1: Transform equation (1):
y = 50 - x
Step 2: Substitute y in equation (2):
0.20x + 0.45(50 - x) = 12.5
Step 3: Solve for x:
0.20x + 22.5 - 0.45x = 12.5
-0.25x = -10
x = 40
Step 4: Substitute x into the transformed equation (1):
y = 50 - 40
y = 10
Therefore, to create the desired 25% acid solution, 40 liters of the 20% acid solution and 10 liters of the 45% acid solution are required.