Solve each problem. See Example.EXAMPLE Solving a Mixture ProblemLisa Harmon is a chemist....

Solve each problem. See Example.

EXAMPLE Solving a Mixture Problem

Lisa Harmon is a chemist. She needs a 20% solution of alcohol. She has a 15% solution on hand, as well as a 30% solution. How many liters of the 15% solution should she add to 3 L of the 30% solution to obtain her 20% solution?

SOLUTION

Step 1 Read the problem. We must find the required number of liters of 15% alcohol solution.

Step 2 Assign a variable.

Let x = the number of liters of 15% solution to be added.

Figure and the table show what is happening in the problem. The numbers in the last column were found by multiplying the strengths and the numbers of liters.

Figure

Step 3 Write an equation. The number of liters of pure alcohol in the 15% solution plus the number of liters in the 30% solution must equal the number of liters in the final 20% solution.

Step 4 Solve.

Step 5 State the answer. Thus, 6 L of 15% solution should be mixed with 3 L of 30% solution, giving 6 + 3 = 9 L of 20% solution.

Step 6 Check. The answer checks, since the amount of alcohol in the two solutions is equal to the amount of alcohol in the mixture.

Acid Mixture Marin Caswell needs 10% hydrochloric acid for a chemistry experiment. How much 5% acid should she mix with 60 mL of 20% acid to get a 10% solution?