Questions: A doctor administers a drug to a 37-kg patient, using a dosage formula of 51 mg / kg / day. Assume that the drug is available in a 100 mg per 5 mL suspension or in 300 mg tablets. a. How many tablets should a 37-kg patient take every four hours? b. The suspension with a drop factor of 10 gtt / mL delivers the drug intravenously to the patient over a twelve-hour period. What flow rate should be used in units of gtthr?

A doctor administers a drug to a 37-kg patient, using a dosage formula of 51 mg / kg / day. Assume that the drug is available in a 100 mg per 5 mL suspension or in 300 mg tablets.
a. How many tablets should a 37-kg patient take every four hours?
b. The suspension with a drop factor of 10 gtt / mL delivers the drug intravenously to the patient over a twelve-hour period. What flow rate should be used in units of gtthr?

Transcript text: A doctor administers a drug to a $37-\mathrm{kg}$ patient, using a dosage formula of $51 \mathrm{mg} / \mathrm{kg} /$ day. Assume that the drug is available in a 100 mg per 5 mL suspension or in 300 mg tablets. a. How many tablets should a $37-\mathrm{kg}$ patient take every four hours? b. The suspension with a drop factor of $10 \mathrm{gtt} / \mathrm{mL}$ delivers the drug intravenously to the patient over a twelve-hour period. What flow rate should be used in units of gtthr?

Solution

Solution Steps

Solution Approach

a. First, calculate the total daily dosage required for the patient by multiplying the patient's weight by the dosage per kilogram. Then, determine the dosage required every four hours by dividing the total daily dosage by the number of four-hour intervals in a day. Finally, calculate the number of tablets needed by dividing the four-hour dosage by the dosage per tablet.

b. Calculate the total daily dosage required for the patient as in part a. Then, determine the total dosage to be delivered over the twelve-hour period. Convert this dosage into milliliters using the suspension concentration. Finally, calculate the flow rate in drops per hour using the drop factor and the total volume to be delivered.

Step 1: Calculate Total Daily Dosage

To determine the total daily dosage required for the patient, multiply the patient's weight by the dosage per kilogram: \[ \text{Total daily dosage} = 37 \, \text{kg} \times 51 \, \frac{\text{mg}}{\text{kg}} = 1887 \, \text{mg} \]

Step 2: Calculate Dosage Every Four Hours

Since there are 6 four-hour intervals in a day, divide the total daily dosage by 6 to find the dosage required every four hours: \[ \text{Four-hour dosage} = \frac{1887 \, \text{mg}}{6} = 314.5 \, \text{mg} \]

Step 3: Determine Number of Tablets Needed

Each tablet contains 300 mg. Divide the four-hour dosage by the dosage per tablet to find the number of tablets needed: \[ \text{Tablets needed} = \frac{314.5 \, \text{mg}}{300 \, \text{mg/tablet}} \approx 1.0483 \] Rounding to the nearest hundredth, the patient should take approximately 1.05 tablets every four hours.

Step 4: Calculate Total Dosage Over Twelve Hours

The total dosage to be delivered over a twelve-hour period is half of the total daily dosage: \[ \text{Twelve-hour dosage} = \frac{1887 \, \text{mg}}{2} = 943.5 \, \text{mg} \]

Step 5: Convert Dosage to Milliliters

The suspension concentration is 100 mg per 5 mL. Convert the twelve-hour dosage to milliliters: \[ \text{Suspension volume} = \frac{943.5 \, \text{mg}}{100 \, \text{mg/5 mL}} \times 5 \, \text{mL} = 47.175 \, \text{mL} \]

Step 6: Calculate Flow Rate in Drops Per Hour

Using a drop factor of 10 gtt/mL, calculate the flow rate in drops per hour over the twelve-hour period: \[ \text{Flow rate} = \frac{47.175 \, \text{mL} \times 10 \, \text{gtt/mL}}{12 \, \text{hours}} \approx 39.3125 \, \text{gtt/hr} \] Rounding to the nearest hundredth, the flow rate should be set to 39.31 gtt/hr.