To determine the quantities of the 50% and 85% acid solutions needed to produce a 75% acid solution, we can set up a system of equations based on the acid concentrations and the desired total volume.
Let's assume the amount of the 50% acid solution needed is x liters, and the amount of the 85% acid solution needed is y liters.
Given:
Total volume = 70 liters
Desired acid concentration = 75%
Based on the acid concentration, we can set up the equation for the acid content:
0.50x + 0.85y = 0.75 * 70
Simplifying the equation, we have:
0.50x + 0.85y = 52.5
We also know that the total volume of the two solutions should be 70 liters:
x + y = 70
Now, we have a system of equations:
0.50x + 0.85y = 52.5 ----(1)
x + y = 70 ----(2)
To solve the system, we can use substitution or elimination method. Here, we'll use the substitution method.
From equation (2), we can express x in terms of y:
x = 70 - y
Substituting this value of x into equation (1):
0.50(70 - y) + 0.85y = 52.5
35 - 0.50y + 0.85y = 52.5
Combining like terms:
0.35y = 17.5
Dividing by 0.35:
y = 50
Substituting the value of y back into equation (2):
x + 50 = 70
x = 20
Therefore, to produce 70 liters of a 75% acid solution, you would need 20 liters of the 50% acid solution and 50 liters of the 85% acid solution.