1. **State the problem:** The theater has a fixed cost of 750 per performance and sells tickets at 8 each. We want to find the minimum number of tickets sold to make a profit of at least 1200. 2. **Define variables and write the profit formula:** Let $x$ be the number of tickets sold. Profit = Revenue - Cost Revenue = $8x$ Cost = 750 Profit = $8x - 750$ 3. **Set up the inequality for profit at least 1200:** $$8x - 750 \geq 1200$$ 4. **Solve the inequality:** Add 750 to both sides: $$8x - \cancel{750} + \cancel{750} \geq 1200 + 750$$ $$8x \geq 1950$$ Divide both sides by 8: $$\frac{8x}{\cancel{8}} \geq \frac{1950}{\cancel{8}}$$ $$x \geq 243.75$$ 5. **Interpret the result:** Since the number of tickets must be a whole number, the theater must sell at least 244 tickets to make a profit of at least 1200. **Final answer:** $$\boxed{244}$$