1. **State the problem:** Hassan and Raju initially have the same number of points. Hassan exchanges 624 points for a prize. After this, Raju has 5 times as many points as Hassan. We need to find how many points Hassan had at first. 2. **Define variables:** Let $x$ be the number of points Hassan (and Raju) had initially. 3. **Write the equation:** After Hassan exchanges 624 points, Hassan's points become $x - 624$. Raju still has $x$ points. According to the problem, Raju's points are 5 times Hassan's points after the exchange: $$x = 5(x - 624)$$ 4. **Solve the equation:** $$x = 5x - 5 \times 624$$ $$x = 5x - 3120$$ 5. **Isolate $x$:** $$x - 5x = -3120$$ $$\cancel{x} - 5\cancel{x} = -3120$$ $$-4x = -3120$$ 6. **Divide both sides by -4:** $$\frac{-4x}{\cancel{-4}} = \frac{-3120}{\cancel{-4}}$$ $$x = 780$$ 7. **Answer:** Hassan had 780 points at first.