# 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?*

*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% 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).