1. **State the problem:** We have 100 students with an average weight of 59 kg. The average weight of boys is 65 kg and that of girls is 50 kg. We need to find the number of boys and girls. 2. **Define variables:** Let $b$ be the number of boys and $g$ be the number of girls. 3. **Write equations:** Since total students are 100, we have: $$b + g = 100$$ The total weight of all students is average weight times number of students: $$59 \times 100 = 5900$$ The total weight can also be expressed as: $$65b + 50g = 5900$$ 4. **Solve the system:** From the first equation, express $g$: $$g = 100 - b$$ Substitute into the second equation: $$65b + 50(100 - b) = 5900$$ Simplify: $$65b + 5000 - 50b = 5900$$ $$15b + 5000 = 5900$$ $$15b = 900$$ $$b = \frac{900}{15} = 60$$ 5. **Find $g$:** $$g = 100 - 60 = 40$$ **Answer:** There are 60 boys and 40 girls in the class.