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How many liters each of a 50 % acid solution and a 85 % acid solution must be used to produce 70 liters of a 75 % acid solution?

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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.

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