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Answer :
Certainly! Let's go through the steps to find the appropriate dose of a drug for a 145-pound person based on the recommended dose of 6.00 mg/kg of body mass. We’ll convert the person’s weight into kilograms first, and then calculate the dosage in milligrams.
### Step-by-Step Solution:
1. Convert Pounds to Kilograms:
- We know that 1 pound is equal to 453.6 grams.
- First, we convert 145 pounds to grams:
[tex]\[
145 \, \text{pounds} \times 453.6 \, \frac{\text{grams}}{\text{pound}} = 65772 \, \text{grams}
\][/tex]
- Since 1 kilogram is 1000 grams, convert grams to kilograms:
[tex]\[
65772 \, \text{grams} \div 1000 = 65.772 \, \text{kilograms}
\][/tex]
2. Calculate the Dose in Milligrams:
- The recommended dose is 6.00 mg/kg.
- To find the dose for a 65.772 kg person:
[tex]\[
6.00 \, \frac{\text{mg}}{\text{kg}} \times 65.772 \, \text{kg} = 394.632 \, \text{mg}
\][/tex]
Therefore, the dose in milligrams for a 145-pound person is approximately 394.632 mg, which is closest to option E) 395 mg when rounded to the nearest whole number.
### Step-by-Step Solution:
1. Convert Pounds to Kilograms:
- We know that 1 pound is equal to 453.6 grams.
- First, we convert 145 pounds to grams:
[tex]\[
145 \, \text{pounds} \times 453.6 \, \frac{\text{grams}}{\text{pound}} = 65772 \, \text{grams}
\][/tex]
- Since 1 kilogram is 1000 grams, convert grams to kilograms:
[tex]\[
65772 \, \text{grams} \div 1000 = 65.772 \, \text{kilograms}
\][/tex]
2. Calculate the Dose in Milligrams:
- The recommended dose is 6.00 mg/kg.
- To find the dose for a 65.772 kg person:
[tex]\[
6.00 \, \frac{\text{mg}}{\text{kg}} \times 65.772 \, \text{kg} = 394.632 \, \text{mg}
\][/tex]
Therefore, the dose in milligrams for a 145-pound person is approximately 394.632 mg, which is closest to option E) 395 mg when rounded to the nearest whole number.
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