A drug is prescribed for an adult weighing 118 pounds at a dose of [tex]30.0 \mu g[/tex] per kilogram of body weight per day in three equal doses. How many micrograms should be administered to the patient at each dose?

Sure! Let’s work through this problem step by step.

1. Convert the weight from pounds to kilograms:

- The patient weighs 118 pounds.
- We need to convert pounds to kilograms. The conversion factor is approximately [tex]\(1 \text{ kilogram} = 2.20462 \text{ pounds}\)[/tex].
- To find out the weight in kilograms, use the formula:
[tex]\[
\text{Weight in kilograms} = \frac{\text{Weight in pounds}}{2.20462}
\][/tex]
- Substituting the given weight:
[tex]\[
\text{Weight in kilograms} = \frac{118}{2.20462} \approx 53.52 \text{ kilograms}
\][/tex]

2. Calculate the total daily dose in micrograms:

- The prescribed dose is [tex]\(30.0 \text{ micrograms per kilogram}\)[/tex] of body weight per day.
- Calculate the total daily dose:
[tex]\[
\text{Total daily dose} = 30.0 \times 53.52 \approx 1605.72 \text{ micrograms}
\][/tex]

3. Determine the dose for each administration:

- The medication is to be administered in three equal doses throughout the day.
- To find out the dose per administration, divide the total daily dose by the number of doses:
[tex]\[
\text{Dose per administration} = \frac{1605.72}{3} \approx 535.24 \text{ micrograms}
\][/tex]

Therefore, the patient should receive approximately 535.24 micrograms of the drug in each dose.