1. **State the problem:** Karen spends money on food, hall, and DJ, then sells tickets. We need to find the percentage profit she makes. 2. **Calculate total cost:** $$\text{Total cost} = 100 + 120 + 80 = 300$$ 3. **Calculate total revenue:** $$\text{Revenue} = 54 \times 7.50 = 405$$ 4. **Calculate profit:** $$\text{Profit} = \text{Revenue} - \text{Total cost} = 405 - 300 = 105$$ 5. **Calculate percentage profit:** $$\text{Percentage profit} = \frac{\text{Profit}}{\text{Total cost}} \times 100 = \frac{105}{300} \times 100$$ 6. **Simplify fraction:** $$\frac{105}{300} = \frac{\cancel{105}}{\cancel{300}} = \frac{7}{20}$$ 7. **Calculate final percentage:** $$\frac{7}{20} \times 100 = 35\%$$ **Final answer:** Karen makes a 35% profit for the charity.