How many liters each of a 15% acid solution and a 85 % acid solution must be used to produce 40 liters of a 50% acid solution?

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  20 liters each

Step-by-step explanation:

Sometimes it is helpful to compare the desired concentration to the average of the constituent concentrations. That average is ...

  (15% +85%)/2 = (100%)/2 = 50%

This is exactly equal to the desired concentration, meaning the mix will be comprised of exactly equal amounts of the constituents.

20 liters each must be used.

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Additional comments

If the average is less than the desired concentration, it means the mix will have more of the most concentrated solution. Similarly, if the average is more than the desired concentration, there must be more of the least concentrated solution. Since the average is exactly equal to the desired concentration, there will not be more of one than the other.

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If you insist on some algebra, let x represent the amount of 85% solution. Then 40-x will be the amount of 15% solution. The amount of acid in the mix is ...

  0.15(40 -x) +0.85x = 0.50(40)

  0.7x +6 = 20 . . . . simplify

  0.7x = 14 . . . . . . . subtract 6

  x = 14/0.7 = 20 . . . . divide by the coefficient of x (liters of 85% acid)

  40-x = 20 . . . . . . . . liters of 15% acid

20 liters of each solution are needed.

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step-by-step explanation:

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