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Answer :
Sure, let's solve the problem step by step:
1. Understand the given information:
- A person weighs 150.0 pounds (lb).
- The dosage of the drug required is 1.50 milligrams (mg) per kilogram (kg) of body weight.
- The conversion factor provided is [tex]\(2.20 \text{ lb} = 1 \text{ kg}\)[/tex].
2. Convert the weight from pounds to kilograms:
- We know [tex]\(1 \text{ kg} = 2.20 \text{ lb}\)[/tex].
- Therefore, to find the weight in kilograms:
[tex]\[
\text{Weight in kg} = \frac{\text{Weight in lb}}{2.20}
\][/tex]
- Plugging in the weight of the person:
[tex]\[
\text{Weight in kg} = \frac{150.0 \text{ lb}}{2.20} = 68.18 \text{ kg}
\][/tex]
3. Calculate the dosage in milligrams:
- The required dosage is [tex]\(1.50 \text{ mg/kg}\)[/tex].
- Therefore, the total dosage required is:
[tex]\[
\text{Dosage (in mg)} = 1.50 \text{ mg/kg} \times 68.18 \text{ kg} = 102.27 \text{ mg}
\][/tex]
4. Round the final answer:
- The calculated dosage [tex]\(102.27 \text{ mg}\)[/tex] rounds to approximately [tex]\(102 \text{ mg}\)[/tex].
So, the correct dosage of the drug that should be given is [tex]\(102 \text{ mg}\)[/tex]. From the options provided, the answer is:
[tex]\[ \boxed{102 \text{ mg}} \][/tex]
1. Understand the given information:
- A person weighs 150.0 pounds (lb).
- The dosage of the drug required is 1.50 milligrams (mg) per kilogram (kg) of body weight.
- The conversion factor provided is [tex]\(2.20 \text{ lb} = 1 \text{ kg}\)[/tex].
2. Convert the weight from pounds to kilograms:
- We know [tex]\(1 \text{ kg} = 2.20 \text{ lb}\)[/tex].
- Therefore, to find the weight in kilograms:
[tex]\[
\text{Weight in kg} = \frac{\text{Weight in lb}}{2.20}
\][/tex]
- Plugging in the weight of the person:
[tex]\[
\text{Weight in kg} = \frac{150.0 \text{ lb}}{2.20} = 68.18 \text{ kg}
\][/tex]
3. Calculate the dosage in milligrams:
- The required dosage is [tex]\(1.50 \text{ mg/kg}\)[/tex].
- Therefore, the total dosage required is:
[tex]\[
\text{Dosage (in mg)} = 1.50 \text{ mg/kg} \times 68.18 \text{ kg} = 102.27 \text{ mg}
\][/tex]
4. Round the final answer:
- The calculated dosage [tex]\(102.27 \text{ mg}\)[/tex] rounds to approximately [tex]\(102 \text{ mg}\)[/tex].
So, the correct dosage of the drug that should be given is [tex]\(102 \text{ mg}\)[/tex]. From the options provided, the answer is:
[tex]\[ \boxed{102 \text{ mg}} \][/tex]
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