Set 16: Systems of Equations (Intermediate)

Choice A is correct. Choice A is the correct answer. Let $a$ = adult tickets and $s$ = student tickets. Step 1: Set up the system: $\begin{cases} a + s = 300 \\ 12 a + 8 s = 2800 \end{cases}$ Step 2: From first equation: $s = 300 - a$ Step 3: Substitute: $$$12a + 8(300 - a) = 2800$12a + 2400 - 8 a = 2800$4a = 400a = 100$$ Solution: 100 adult tickets (and 200 student tickets) Verification: $$100+ 200 = 300$$ ✓ and 12(100) + 8(200) = 1200 + 1600 = 2800$✓ Strategic Tip: Revenue problems: tickets × price = total revenue. Choice B is incorrect because$12(150) + 8(150) = 1800 + 1200 = 3000 \neq 2800$. Choice C is incorrect because$12(125) + 8(175) = 1500 + 1400 = 2900 \neq 2800$. Choice D is incorrect because$12(175) + 8(125) = 2100 + 1000 = 3100 \neq 2800$.