Questions: A child with an allergie reaction is administered diphenhydramine (Benadryl). The manufacturer recommends a dosage of 6.25 mg / kg for each dose. If the child weighing 46 lbs is given 1 dose each day, how much diphenhydramine in milligrams would they have taken in a week? (1 kg=2.205 lbs)

Solution Steps

To convert the child's weight from pounds to kilograms, we use the conversion factor \( 1 \, \text{kg} = 2.205 \, \text{lbs} \). Thus, the weight in kilograms is calculated as: \[ \text{weight}_{\text{kg}} = \frac{\text{weight}_{\text{lbs}}}{2.205} = \frac{46}{2.205} \approx 20.8617 \, \text{kg} \]

The recommended dosage of diphenhydramine is \( 6.25 \, \text{mg/kg} \). Therefore, the daily dosage in milligrams is given by: \[ \text{daily dosage}_{\text{mg}} = \text{weight}_{\text{kg}} \times 6.25 = 20.8617 \times 6.25 \approx 130.3855 \, \text{mg} \]

To find the total amount of diphenhydramine taken in a week, we multiply the daily dosage by the number of days in a week: \[ \text{weekly dosage}_{\text{mg}} = \text{daily dosage}_{\text{mg}} \times 7 = 130.3855 \times 7 \approx 912.6984 \, \text{mg} \]

Final Answer