1. **State the problem:** We need to find a system of inequalities representing the number of ushers ($x$) and tech crew members ($y$) based on hours worked and uniforms available. 2. **Given information:** - Ushers work 3-hour shifts: total usher hours = $3x$ - Tech crew work 6-hour shifts: total tech crew hours = $6y$ - Total volunteer hours must be less than 60: $$3x + 6y < 60$$ - Theatre has 12 uniforms total - Each usher needs 1 uniform: $x$ uniforms - Each tech crew member needs 2 uniforms: $2y$ uniforms - Total uniforms used must be less than or equal to 12: $$x + 2y \leq 12$$ 3. **Analyze the options:** - The hours inequality must be strict less than 60, so $3x + 6y < 60$ - The uniform inequality must be $x + 2y \leq 12$ because the theatre only has 12 uniforms available, so the total uniforms used cannot exceed 12. 4. **Conclusion:** The correct system is: $$\begin{cases} 3x + 6y < 60 \\ x + 2y \leq 12 \end{cases}$$ This matches option B. **Final answer:** Option B