Set 15: Systems of Equations

Choice C is correct. Choice C is the correct answer. Let $p$ be the number of people. Service 1: $C_1 = 200 + 25 p$ Service 2: $C_2 = 150 + 30 p$ Set equal: $$$200+ 25 p = 150 + 30 p$200- 150 = 30 p - 25 p$50= 5 pp = 10$$ Solution: 10 people Verification: - Service 1: $$200+ 25(10) = 450$$ - Service 2: $$150+ 30(10) = 450$$ ✓ Strategic Tip: Break-even analysis finds where two linear models intersect. Choice A is incorrect because at 8: Service 1 = 400, Service 2 = $390. Choice B is incorrect because at 12: Service 1 =$500, Service 2 = $510. Choice D is incorrect because at 15: Service 1 =$575, Service 2 = $600.