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If a 163-pound man can have 1425 mg of a medicine in a day, how much can a 117-pound woman have?

(Round the answer to one decimal place.)

Answer :

To solve this problem, the key is determining how much medicine is allotted per pound of body weight and then applying that information to the woman's weight. Here's a step-by-step breakdown:

1. Calculate the medicine per pound for the man:

- The man weighs 163 pounds and can have 1425 mg of medicine.
- To find out how much medicine corresponds to each pound of his body weight, you divide 1425 mg by 163 pounds:

[tex]\[
\text{Medicine per pound} = \frac{1425 \, \text{mg}}{163 \, \text{pounds}} \approx 8.74 \, \text{mg/pound}
\][/tex]

2. Calculate the appropriate dosage for the woman:

- The woman weighs 117 pounds.
- Use the amount of medicine per pound (8.74 mg/pound) to find out how much medicine she should take:

[tex]\[
\text{Woman's medicine} = 8.74 \, \text{mg/pound} \times 117 \, \text{pounds} \approx 1022.9 \, \text{mg}
\][/tex]

Thus, the 117-pound woman can have approximately 1022.9 mg of the medicine in a day, when rounded to one decimal place.

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