**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.

**Example:**

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?

(A) 20

(B) 30

(C) 40

(D) 50

(E) 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% Â· 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% Â· 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).