Answer :
To solve the problem of determining how many capsules are needed, let's go through the steps step-by-step.
1. Convert Weight from Pounds to Kilograms:
- The weight of the person is 165 pounds.
- To convert pounds to kilograms, use the conversion factor: [tex]\(1 \text{ lb} = 0.453592 \text{ kg}\)[/tex].
- Multiply the weight in pounds by the conversion factor:
[tex]\[
\text{Weight in kg} = 165 \times 0.453592 = 74.84268 \text{ kg}
\][/tex]
2. Calculate the Dosage Required per Day:
- The dosage required is 50 mg of clarithromycin per kg of body weight, per day.
- Multiply the person's weight in kilograms by the dosage per kilogram:
[tex]\[
\text{Daily dosage in mg} = 50 \times 74.84268 = 3742.134 \text{ mg/day}
\][/tex]
3. Calculate the Total Dosage Required for 10 Days:
- Multiply the daily dosage by the number of days (10 days):
[tex]\[
\text{Total dosage in mg} = 3742.134 \times 10 = 37421.34 \text{ mg}
\][/tex]
4. Determine the Number of Capsules Needed:
- Each capsule contains 250 mg of clarithromycin.
- Divide the total dosage required by the amount of clarithromycin per capsule to find the number of capsules needed:
[tex]\[
\text{Capsules needed} = \frac{37421.34}{250} = 149.68536
\][/tex]
Since we cannot have a fraction of a capsule, we need to round up to the nearest whole number. Therefore, a total of 150 capsules are needed to provide the required dosage over 10 days.
1. Convert Weight from Pounds to Kilograms:
- The weight of the person is 165 pounds.
- To convert pounds to kilograms, use the conversion factor: [tex]\(1 \text{ lb} = 0.453592 \text{ kg}\)[/tex].
- Multiply the weight in pounds by the conversion factor:
[tex]\[
\text{Weight in kg} = 165 \times 0.453592 = 74.84268 \text{ kg}
\][/tex]
2. Calculate the Dosage Required per Day:
- The dosage required is 50 mg of clarithromycin per kg of body weight, per day.
- Multiply the person's weight in kilograms by the dosage per kilogram:
[tex]\[
\text{Daily dosage in mg} = 50 \times 74.84268 = 3742.134 \text{ mg/day}
\][/tex]
3. Calculate the Total Dosage Required for 10 Days:
- Multiply the daily dosage by the number of days (10 days):
[tex]\[
\text{Total dosage in mg} = 3742.134 \times 10 = 37421.34 \text{ mg}
\][/tex]
4. Determine the Number of Capsules Needed:
- Each capsule contains 250 mg of clarithromycin.
- Divide the total dosage required by the amount of clarithromycin per capsule to find the number of capsules needed:
[tex]\[
\text{Capsules needed} = \frac{37421.34}{250} = 149.68536
\][/tex]
Since we cannot have a fraction of a capsule, we need to round up to the nearest whole number. Therefore, a total of 150 capsules are needed to provide the required dosage over 10 days.
