1. **State the problem:** The drama club sells student tickets at $6.50 each and adult tickets at $9 each. They sold 63 adult tickets and want to find the possible number of student tickets sold to meet at least $920 in total revenue. The auditorium capacity is 120 people. 2. **Define variables:** Let $x$ be the number of student tickets sold. 3. **Write inequalities based on the problem:** - Total people cannot exceed 120: $$x + 63 \leq 120$$ - Total revenue must be at least 920: $$6.5x + 9 \times 63 \geq 920$$ 4. **Solve the first inequality for $x$:** $$x + 63 \leq 120$$ $$x \leq 120 - 63$$ $$x \leq 57$$ 5. **Calculate revenue from adult tickets:** $$9 \times 63 = 567$$ 6. **Solve the revenue inequality for $x$:** $$6.5x + 567 \geq 920$$ $$6.5x \geq 920 - 567$$ $$6.5x \geq 353$$ $$x \geq \frac{353}{6.5}$$ $$x \geq 54.3077...$$ 7. **Combine both inequalities for $x$:** $$54.3077... \leq x \leq 57$$ 8. **Interpretation:** Since $x$ must be a whole number (tickets sold), the drama club must sell at least 55 and at most 57 student tickets to meet the expenses and not exceed auditorium capacity. **Final answer:** $$\boxed{55 \leq x \leq 57}$$