Set 10: Systems of Equations

Choice D is correct. Choice D is the correct answer. Let $r$ = regular tickets and $v$ = VIP tickets. System: $\begin{cases} r + v = 120 \\ 5 r + 15 v = 1000 \end{cases}$ Step 1: From first: $r = 120 - v$ Step 2: Substitute: 5(120 - v) + 15 v = 1000$600- 5 v + 15 v = 100010v = 400v = 40$$ Solution: 40 VIP tickets (and 80 regular tickets) Verification: $$80+ 40 = 120$$ ✓ and 5(80) + 15(40) = 400 + 600 = 1000$ ✓ Strategic Tip: Ticket problems combine quantity and revenue equations. Other choices fail verification.