1. **State the problem:** We have 33 students divided into two groups A and B. 2. **Given condition:** 5 times the number of students in group A equals 6 times the number in group B. 3. **Let:** - Number of students in group A = $x$ - Number of students in group B = $y$ 4. **Write the equations:** - Total students: $$x + y = 33$$ - Given relation: $$5x = 6y$$ 5. **Express $x$ in terms of $y$ from the second equation:** $$5x = 6y \implies x = \frac{6y}{5}$$ 6. **Substitute $x$ into the total students equation:** $$\frac{6y}{5} + y = 33$$ 7. **Combine like terms:** $$\frac{6y}{5} + \frac{5y}{5} = 33$$ $$\frac{11y}{5} = 33$$ 8. **Solve for $y$:** $$y = 33 \times \frac{5}{11}$$ $$y = 3 \times 5 = 15$$ 9. **Find $x$ using $x = \frac{6y}{5}$:** $$x = \frac{6 \times 15}{5} = \frac{90}{5} = 18$$ 10. **Find the difference between the numbers of students in groups A and B:** $$|x - y| = |18 - 15| = 3$$ **Final answer:** The difference between the numbers of students in groups A and B is 3.