Solve the problem by setting up and solving an appropriate algebraic equation.

Question

A pharmacist has a 4% solution of cough syrup and a 16% solution of the same cough syrup. How many ounces of each must be mixed to make 16 ounces of a 10% solution of cough syrup?

4% solution ____ oz

16% solution ____ oz

Answer 1

8 ounces of each solution combine to give 16 ounces of 10% solution

16(.10)=x(.04)+(16-x)(.16)

1.6=.04x+2.56-.16x

2.56-1.6=.16x-.04x

0.96=0.12x

x=0.96/0.12 = 96/12= 8 ounces of 4% solution

16-x=16-8= 8 ounces of 16% solution

Or more simply, you might notice that 4% is 6% less than 10% and

also notice 16% is 6% more than 10%. Both initial solutions are exactly 6%

away from the desired 10%. Just combine equal quantities of each.

Since you want 16 ounces as the end product, then 8+8=16 ounces.