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?
To prepare 100 mL of a solution with a drug concentration of 2 mg/mL, we need to determine how much of the drug and cherry flavored syrup to use.
Let's assume the amount of drug needed is x mL.
To find how much cherry flavored syrup to add, we subtract the amount of drug solution from the total volume of the desired solution:
Total volume - drug volume = cherry syrup volume
100 mL - x mL = cherry syrup volume
Now, let's focus on the concentrations of the drug in the drug solution and the desired solution. According to the problem statement, the drug concentration in the elixir is 5 mg/mL, and we want a drug concentration of 2 mg/mL in the final solution.
We can relate the amount of drug and the drug concentration with the following formula:
Amount of drug = concentration of drug × volume
In the drug solution, the concentration is 5 mg/mL, and the volume is x mL. Therefore, the amount of drug in the drug solution is 5x mg.
In the final solution, the concentration is 2 mg/mL, and the volume is 100 mL. Therefore, the amount of drug in the final solution is 2 × 100 = 200 mg.
Since the amount of drug is the same in both the drug solution and the final solution, we can equate these two amounts:
5x mg = 200 mg
Solving for x, we find:
x = 200 mg / 5
x = 40 mL
Therefore, we need to use 40 mL of the drug solution and the remaining volume (100 mL - 40 mL = 60 mL) of cherry flavored syrup to prepare 100 mL of the solution with a drug concentration of 2 mg/mL.