If this situation is modeled as a system of equations and graphed, what does the intersection point represent in this real-world context? Answer: The theater sells 50 adult tickets and 50 student tickets to meet both the ticket count and revenue requirements
The system is: a + s = 100 (total tickets) and 12a + 8s = 1000 (total revenue), where a = adult tickets and s = student tickets. Solving: from the first equation, s = 100 - a. Substituting: 12a + 8(100 - a) = 1000, so 12a + 800 - 8a = 1000, giving 4a = 200, so a = 50 and s = 50. Verification: 50 + 50 = 100 tickets ✓ and 12(50) + 8(50) = 600 + 400 = 1000 ✓. The intersection represents the unique combination that satisfies both constraints simultaneously. Choice A mentions profit maximization which isn't specified. Choices B and C give incorrect ticket combinations.
