College

A certain drug dosage calls for 15 mg per kg per day and is divided into three doses (one every 8 hours). If a person weighs 195 pounds, how much of the drug should be administered each time?

Express your answer rounded up to the next milligram.

___ mg

Answer :

To determine how much of the drug should be administered in each dose, we need to follow these steps:

1. Convert the person's weight from pounds to kilograms:
- A person weighs 195 pounds. To convert pounds to kilograms, we use the conversion factor 1 pound = 0.453592 kilograms.
- So, the weight in kilograms is [tex]\( 195 \times 0.453592 = 88.45044 \)[/tex] kg.

2. Calculate the total daily dosage needed:
- The drug dosage required is 15 mg per kg of body weight per day.
- Multiply the person's weight in kilograms by the dosage per kg:
[tex]\[
88.45044 \, \text{kg} \times 15 \, \text{mg/kg/day} = 1326.7566 \, \text{mg/day}
\][/tex]

3. Determine the dosage per dose:
- The daily dosage needs to be divided into three doses, since they are administered every 8 hours (3 times a day).
- So, the dosage per dose is:
[tex]\[
\frac{1326.7566 \, \text{mg}}{3} = 442.2522 \, \text{mg/dose}
\][/tex]

4. Round up to the nearest whole milligram:
- To ensure the proper dosage is given, we round up to the next milligram, resulting in 443 mg per dose.

Therefore, the amount of the drug that should be administered each time is 443 mg.