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.

Question

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.

Answer 1

To find the dose in drops for the child, we first need to calculate the total amount of cough syrup the child needs to receive.

The dose of dextromethorphan HBr for the child is 1.5 mg. We know that the concentration of dextromethorphan HBr in the cough syrup is 30 mg/15 mL. We can set up a proportion to find the amount of cough syrup needed:

1.5 mg / x mL = 30 mg / 15 mL

Cross-multiplying and solving for x, we get:

x = (1.5 mg * 15 mL) / (30 mg)
x = 0.75 mL

So the child needs to receive 0.75 mL of cough syrup.

Next, we need to determine the number of drops in 0.75 mL. We know that the medicine dropper delivers 20 drops per 1 mL. So for 0.75 mL, we can calculate the number of drops:

0.75 mL * 20 drops/mL = 15 drops

Therefore, the dose for the child is 15 drops.