Set 16: Systems of Equations (Advanced)

Choice C is correct. Choice C is the correct answer. Let $f$ = floor seats and $b$ = balcony seats. System: $\begin{cases} f + b = 400 \\ 75 f + 45 b = 22500 \end{cases}$ Step 1: From first: $b = 400 - f$ Step 2: Substitute: $$$75f + 45(400 - f) = 22500$75f + 18000 - 45 f = 22500$30f = 4500f = 150$$ Solution: 150 floor seats (and 250 balcony seats) Verification: $$150+ 250 = 400$$ ✓ and 75(150) + 45(250) = 11250 + 11250 = 22500$✓ Strategic Tip: Revenue problems: quantity × price = total revenue. Choice A is incorrect because$75(100) + 45(300) = 7500 + 13500 = 21000 \neq 22500$. Choice B is incorrect because$75(125) + 45(275) = 9375 + 12375 = 21750 \neq 22500$. Choice D is incorrect because$75(175) + 45(225) = 13125 + 10125 = 23250 \neq 22500$.