Question

A doctor prescribes an ointment that is 4% hydrocortisone. A pharmacist has 1% and 5% concentrations in stock. How many ounces of each should the pharmacist use to make a 2 ounce tube?

Answer 1

Let x be the amount of the 1% concentration used. Let y be the amount of the 5% concentration used.

The concentration of the two mixed will be the average amount of hydrocortisone per ounce. To find the average take (0.01x + 0.05y)/(x+y). You know that this expression needs to equal 0.04, since you're aiming for a 4% concentration. You also know that x + y must equal 2 since the pharmacist needs to make a 2 ounce tube of the ointment. This means that 0.01x + 0.05y must equal 0.04 since the denominator x + y is 1.

So now you have a system of 2 linear equations:
0.01x + 0.05y = 0.04
x + y= 2

Multiply both sides of the top equation by 100 to get:
x + 5y = 4
x + y = 2

Subtract the bottom equation from the top equation to get:
4y = 2

So y = 2/4=1/2 ounces and therefore x = 3/2 ounce.