A physician asks a pharmacist to calculate the dose of a cough syrup so that it may be safely administered drop wise to a child. The cough syrup contains the active ingredient dextromethorphan HBr, 30 mg/15 mL, in a 120-mL bottle. Based on the child’s weight and literature references, the pharmacist determines the dose of dextromethorphan HBr to be 1.5 mg for the child. The medicine dropper to be dispensed with the medication is calibrated by the pharmacist and shown to deliver 20 drops of the cough syrup per 1 mL. Calculate the dose, in drops, for the child.
The dose of dextromethorphan HBr for the child is 1.5 mg.
The concentration of dextromethorphan HBr in the cough syrup is 30 mg/15 mL.
To find the volume of cough syrup needed to deliver 1.5 mg of dextromethorphan HBr, we can set up a proportion:
30 mg / 15 mL = 1.5 mg / x mL
Cross multiplying, we get:
30 mg * x mL = 1.5 mg * 15 mL
30x = 22.5
x = 22.5 / 30
x = 0.75 mL
Since the medicine dropper delivers 20 drops per 1 mL, the dose for the child in drops is:
0.75 mL * 20 drops/mL = 15 drops.
Therefore, the dose for the child is 15 drops.