Mixture ProblemsThe 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?
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% β 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% β 50 + 30%x = 20%(50 + x)
Multiply this equation by 100 to clear the percent symbol and then solving for ΞΎ yields x = 50.
The answer is (D).