1. **State the problem:** A man shared livestock among three children: Ama, Kofi, and Yaw. Ama had $\frac{2}{5}$ of the livestock, Kofi had $\frac{3}{7}$ of the livestock, and Yaw had 20 livestock. We need to find: A. The total number of livestock shared. B. How many livestock each child got. 2. **Define variables:** Let the total number of livestock be $x$. 3. **Express the shares:** - Ama's share = $\frac{2}{5}x$ - Kofi's share = $\frac{3}{7}x$ - Yaw's share = 20 4. **Write the equation for total livestock:** $$\frac{2}{5}x + \frac{3}{7}x + 20 = x$$ 5. **Find a common denominator for the fractions:** The denominators are 5 and 7, so the common denominator is 35. Rewrite the fractions: $$\frac{2}{5}x = \frac{14}{35}x, \quad \frac{3}{7}x = \frac{15}{35}x$$ 6. **Substitute back into the equation:** $$\frac{14}{35}x + \frac{15}{35}x + 20 = x$$ 7. **Combine the fractions:** $$\frac{14 + 15}{35}x + 20 = x$$ $$\frac{29}{35}x + 20 = x$$ 8. **Isolate $x$:** $$20 = x - \frac{29}{35}x = \frac{35}{35}x - \frac{29}{35}x = \frac{6}{35}x$$ 9. **Solve for $x$:** $$x = \frac{20 \times 35}{6} = \frac{700}{6} = \frac{350}{3} \approx 116.67$$ Since the number of livestock must be a whole number, we check if the problem allows fractional livestock or if the problem expects rounding. Assuming exact division, the total livestock is $\frac{350}{3}$. 10. **Calculate each child's share:** - Ama: $\frac{2}{5} \times \frac{350}{3} = \frac{2}{5} \times \frac{350}{3} = \frac{700}{15} = \frac{140}{3} \approx 46.67$ - Kofi: $\frac{3}{7} \times \frac{350}{3} = \frac{3}{7} \times \frac{350}{3} = \frac{350}{7} = 50$ - Yaw: 20 (given) 11. **Summary:** - Total livestock shared: $\frac{350}{3}$ (approximately 116.67) - Ama's share: $\frac{140}{3}$ (approximately 46.67) - Kofi's share: 50 - Yaw's share: 20 If the problem expects whole numbers, the shares may need adjustment or the problem data may be inconsistent.