An asthma medicine is to be prepared from an elixir with a drug concentration of 5 mg/mL and a cherry flavored syrup that is to be added to hide the taste of the drug. How much of each must be used to prepare 100 mL of solution with a drug concentration of 2 mg/mL?

Question

An asthma medicine is to be prepared from an elixir with a drug concentration of 5 mg/mL and a cherry flavored syrup that is to be added to hide the taste of the drug. How much of each must be used to prepare 100 mL of solution with a drug concentration of 2 mg/mL?

Answer 1

If x mL of 5% solution is used, add up the drug amount in the elixir and the syrup. It must equal the drug amount in the final solution:

5x + 0 = 2(100)
x = 40

So, 40mL of elixir and 60mL of syrup

Or, think of it as obtaining 2/5 the concentration, so we need 5/2 the volume. 5/2(40) = 100