1. **State the problem:** We need to find what percentage of the 4500 seats were filled by the 6th graders. 2. **Identify given information:** - Total seats in theater: $4500$ - Vacant seats: $3105$ 3. **Find the number of seats filled:** $$\text{Seats filled} = 4500 - 3105 = 1395$$ 4. **Use the percentage formula:** $$\text{Percentage filled} = \left(\frac{\text{Seats filled}}{\text{Total seats}}\right) \times 100$$ 5. **Substitute values:** $$\text{Percentage filled} = \left(\frac{1395}{4500}\right) \times 100$$ 6. **Simplify the fraction:** $$\frac{1395}{4500} = \frac{\cancel{1395}}{\cancel{4500}} = \frac{1395 \div 15}{4500 \div 15} = \frac{93}{300}$$ 7. **Further simplify:** $$\frac{93}{300} = \frac{\cancel{93}}{\cancel{300}} = \frac{93 \div 3}{300 \div 3} = \frac{31}{100}$$ 8. **Calculate the percentage:** $$\frac{31}{100} \times 100 = 31\%$$ **Final answer:** The 6th graders filled 31% of the seats in the theater.