1. **State the problem:** Jason bought a sack of rice weighing more than 25kg but less than 60kg. He packed the rice into 5kg bags and had 1kg left over. He packed the rice into 6kg bags and had 2kg left over. We need to find the exact weight of the rice. 2. **Set up the equations:** Let the weight of the rice be $x$ kg. From the problem: - When divided by 5, remainder is 1: $$x \equiv 1 \pmod{5}$$ - When divided by 6, remainder is 2: $$x \equiv 2 \pmod{6}$$ Also, $$25 < x < 60$$ 3. **Solve the congruences:** From $$x \equiv 1 \pmod{5}$$, possible values are: $$x = 5k + 1$$ for some integer $k$. 4. **Check values for $$x = 5k + 1$$ between 25 and 60:** - For $k=5$, $x=26$ - $k=6$, $x=31$ - $k=7$, $x=36$ - $k=8$, $x=41$ - $k=9$, $x=46$ - $k=10$, $x=51$ - $k=11$, $x=56$ 5. **Check which of these satisfy $$x \equiv 2 \pmod{6}$$:** Calculate $x \mod 6$: - $26 \mod 6 = 2$ (valid) - $31 \mod 6 = 1$ - $36 \mod 6 = 0$ - $41 \mod 6 = 5$ - $46 \mod 6 = 4$ - $51 \mod 6 = 3$ - $56 \mod 6 = 2$ (valid) 6. **Check which valid values are between 25 and 60:** Both 26 and 56 satisfy the conditions. 7. **Conclusion:** Jason bought either 26 kg or 56 kg of rice. Since both satisfy the problem conditions, these are the possible weights. **Final answer:** $$\boxed{26 \text{ kg or } 56 \text{ kg}}$$