1. **State the problem:** Leon has a total salary of 6000. He spends 800 on bills, 800 on entertainment, and saves 1200. He spends twice as much on food as on transport. He spends 500 less on rent than on food. Find the amounts spent on food, transport, and rent. 2. **Define variables:** Let $T$ = amount spent on transport. Then, food $F = 2T$. Rent $R = F - 500 = 2T - 500$. 3. **Set up the budget equation:** Total salary = sum of all expenses and savings. $$6000 = 800 \text{ (bills)} + 800 \text{ (entertainment)} + 1200 \text{ (savings)} + F + T + R$$ Substitute $F$ and $R$: $$6000 = 800 + 800 + 1200 + 2T + T + (2T - 500)$$ 4. **Simplify:** $$6000 = 2800 + 5T - 500$$ $$6000 = 2300 + 5T$$ Subtract 2300 from both sides: $$6000 - 2300 = 5T$$ $$3700 = 5T$$ 5. **Solve for $T$:** $$T = \frac{3700}{5} = 740$$ 6. **Find $F$ and $R$:** $$F = 2T = 2 \times 740 = 1480$$ $$R = F - 500 = 1480 - 500 = 980$$ 7. **Final answer:** Leon spends $\boxed{1480}$ on food, $\boxed{740}$ on transport, and $\boxed{980}$ on rent.