1. **State the problem:** We need to find how many people should be summoned so that about 60 people remain in the jury pool after accounting for those who appear and those excused. 2. **Define variables and given data:** - Let $X$ be the number of people summoned. - 40% of summoned people appear, so number appeared is $0.4X$. - Of those who appear, 1/3 are excused, so number excused is $\frac{1}{3} \times 0.4X = \frac{0.4X}{3}$. - The jury pool consists of those who appeared but were not excused, so jury pool size is $0.4X - \frac{0.4X}{3}$. 3. **Set up the equation:** We want the jury pool size to be about 60: $$0.4X - \frac{0.4X}{3} = 60$$ 4. **Simplify the equation:** $$0.4X \left(1 - \frac{1}{3}\right) = 60$$ $$0.4X \times \frac{2}{3} = 60$$ $$\frac{0.8X}{3} = 60$$ 5. **Solve for $X$:** $$0.8X = 60 \times 3$$ $$0.8X = 180$$ $$X = \frac{180}{0.8} = 225$$ 6. **Interpretation:** To have about 60 people in the jury pool, approximately 225 people should be summoned. **Final answer:** $$\boxed{225}$$