Answer :
A 152-pound woman can have approximately 596.18 mg of the medicine in a day, based on the dosage prescribed for a 181-pound man.
To determine how much medicine a 152-pound woman can have based on the dosage for a 181-pound man, we can use the concept of proportionality based on their weights.
Given:
- A 181-pound man can have 709 mg of medicine per day.
We need to find out how much a 152-pound woman can have.
First, establish a proportion based on their weights:
- [tex]\[ \frac{\text{Amount for man}}{\text{Weight of man}} = \frac{\text{Amount for woman}}{\text{Weight of woman}} \][/tex]
Let x be the amount of medicine the 152-pound woman can have.
Set up the proportion:
- [tex]\[ \frac{709 \text{ mg}}{181 \text{ pounds}} = \frac{x \text{ mg}}{152 \text{ pounds}} \][/tex]
Now, solve for x :
- [tex]\[ x = \frac{709 \times 152}{181} \][/tex]
- [tex]\[ x = \frac{107948}{181} \][/tex]
- [tex]\[ x \approx 596.18 \text{ mg} \][/tex]
Therefore, a 152-pound woman can have approximately 596.18 mg of the medicine in a day, based on the dosage prescribed for a 181-pound man.
