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Mixture Problems

The key to these problems is that the combined total of the concentrations in the two parts must be the same as the whole mixture.

How many ounces of a solution that is 30 percent salt must be added to a 50-ounce solution that is 10 percent salt so that the resulting solution is 20 percent salt?

  1. 20
  2. 30
  3. 40
  4. 50
  5. 60

Let x be the ounces of the 30 percent solution.
Then 30%x is the amount of salt in that solution.
The final solution will be 50 + x ounces, and its concentration of salt will be 20%(50 + x).
The original amount of salt in the solution is 10% — 50.
Now, the concentration of salt in the original solution plus the concentration of salt in the added solution must equal the concentration of salt in the resulting solution:

10% — 50 + 30%x = 20%(50 + x)

Multiply this equation by 100 to clear the percent symbol and then solving for x yields x = 50.


The answer is (D).

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