College

A person weighs 150.0 lb, and the correct dosage of a drug is given as 1.50 mg per kilogram of body weight. How many milligrams of the drug should be given? (2.20 lb = 1 kg)

A. 115 mg
B. 112 mg
C. None of the above
D. 102 mg
E. 108 mg

Answer :

To find the correct dosage of the drug for a person weighing 150.0 pounds, we'll follow these steps:

1. Convert the person's weight from pounds to kilograms:
- We know the conversion factor between pounds and kilograms is [tex]\(1 \text{ kg} = 2.20 \text{ lb}\)[/tex].
- To convert the weight from pounds to kilograms, we use the formula:
[tex]\[
\text{Weight in kilograms} = \frac{\text{Weight in pounds}}{\text{Conversion factor}}
\][/tex]
- Plug in the values:
[tex]\[
\text{Weight in kilograms} = \frac{150.0 \text{ lb}}{2.20 \text{ lb/kg}} \approx 68.18 \text{ kg}
\][/tex]

2. Calculate the dosage in milligrams based on the body weight in kilograms:
- The dosage required is 1.50 mg per kilogram of body weight.
- We use the formula:
[tex]\[
\text{Dosage in milligrams} = \text{Dosage per kg} \times \text{Weight in kilograms}
\][/tex]
- Substitute the values:
[tex]\[
\text{Dosage in milligrams} = 1.50 \text{ mg/kg} \times 68.18 \text{ kg} \approx 102.27 \text{ mg}
\][/tex]

In conclusion, the person should be given approximately 102 mg of the drug. Therefore, the correct answer from the given options is 102 mg.

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