1. **State the problem:** We know a 162 pound man can have 1016 mg of a medicine in a day. We want to find how much medicine a 161 pound woman can have, assuming the dosage is proportional to body weight. 2. **Formula used:** The dosage is proportional to weight, so: $$\frac{\text{Dosage}_1}{\text{Weight}_1} = \frac{\text{Dosage}_2}{\text{Weight}_2}$$ 3. **Set up the proportion:** Let $x$ be the dosage for the 161 pound woman. $$\frac{1016}{162} = \frac{x}{161}$$ 4. **Solve for $x$:** Multiply both sides by 161: $$x = \frac{1016}{162} \times 161$$ 5. **Simplify the fraction:** $$x = 1016 \times \frac{161}{162}$$ 6. **Calculate the value:** $$x = 1016 \times 0.9938 = 1009.4$$ 7. **Final answer:** The 161 pound woman can have approximately **1009.4 mg** of the medicine in a day.