Set 11: Systems of Equations (Intermediate)

Choice C is correct. Choice C is the correct answer. Let $s$ be the number of sessions. Set up equations for total cost at each gym. Gym 1: $C_1 = 50 + 5 s$ Gym 2: $C_2 = 30 + 10 s$ Set equal (cost is the same): $$$50+ 5 s = 30 + 10 s$50- 30 = 10 s - 5 s$20= 5 ss = 4$$ Solution: 4 sessions Verification: - Gym 1: $$50+ 5(4) = 70$$ - Gym 2: $$30+ 10(4) = 70$$ ✓ Strategic Tip: "Break-even" problems ask where two expressions are equal. Choice A is incorrect because at 3 sessions: Gym 1 = 65, Gym 2 = 60 dollars (not equal). Choice B is incorrect because at 5 sessions: Gym 1 = $75, Gym 2 = 80 dollars (not equal). Choice D is incorrect because at 6 sessions: Gym 1 =$80, Gym 2 = 90 dollars (not equal).