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how many liters each of a 50% acid solution and a 65% acid solution must be used to produce 60 liters of a 55% acid solution?

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Final answer:

To produce 60 liters of a 55% acid solution, you will need 40 liters of a 50% acid solution and 20 liters of a 65% acid solution.

Step-by-step explanation:

To find out how many liters each of a 50% acid solution and a 65% acid solution must be used to produce 60 liters of a 55% acid solution, we can set up a system of equations using the principle of conservation of mass. Let's denote the amount of the 50% solution as x liters, and the amount of the 65% solution as y liters. The total volume of the resulting solution should be 60 liters, so we have the equation: x + y = 60. We also know that the amount of acid in the resulting solution should be 55% of the total volume, so we have the equation: 0.5x + 0.65y = 0.55 * 60. Now, we can solve this system of equations:

  1. From the first equation, we can express x in terms of y: x = 60 - y.
  2. Substitute this expression for x into the second equation: 0.5(60 - y) + 0.65y = 0.55 * 60.
  3. Simplify and solve for y: 30 - 0.5y + 0.65y = 33.
  4. Combine like terms: 0.15y = 3.
  5. Divide both sides by 0.15 to isolate y: y = 20.
  6. Substitute this value of y back into the equation x = 60 - y: x = 60 - 20.
  7. Simplify: x = 40.

Therefore, you will need 40 liters of the 50% acid solution and 20 liters of the 65% acid solution to produce 60 liters of a 55% acid solution.

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