To produce 70 liters of a 75% acid solution, we need to mix a 50% acid solution and an 85% acid solution in the right proportions. Let x be the number of liters of the 50% acid solution, and y be the number of liters of the 85% acid solution.
We can set up a system of two equations to represent the problem:
x + y = 70 (the total volume of the mixture is 70 liters)
0.5x + 0.85y = 0.75(70) (the total amount of acid in the mixture is 75% of 70 liters)
Simplifying the second equation, we get:
0.5x + 0.85y = 52.5
Now we can solve for x and y using the system of equations. One way to do this is to multiply the first equation by 0.5 and subtract it from the second equation:
0.5x + 0.85y = 52.5
-0.5x - 0.5y = -35
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0.35y = 17.5
y = 50
So we need 50 liters of the 85% acid solution. Substituting this value into the first equation, we get:
x + 50 = 70
x = 20
Therefore, we need 20 liters of the 50% acid solution and 50 liters of the 85% acid solution to produce 70 liters of a 75% acid solution.