5
algebra

A fundraiser sold raffle tickets. Regular tickets cost $5 and VIP tickets cost $15. They sold 120 tickets for $1,000. How many VIP tickets were sold?

A

25 VIP tickets

B

30 VIP tickets

C

35 VIP tickets

D

40 VIP tickets

Correct Answer: D

Choice D is the correct answer. Let rr = regular tickets and vv = VIP tickets.

System: {r+v=1205r+15v=1000\begin{cases} r + v = 120 \\ 5r + 15v = 1000 \end{cases}

Step 1: From first: r=120vr = 120 - v

Step 2: Substitute: 5(120v)+15v=10005(120 - v) + 15v = 10006005v+15v=1000600 - 5v + 15v = 100010v=40010v = 400v=40v = 40

Solution: 40 VIP tickets (and 80 regular tickets)

Verification: 80+40=12080 + 40 = 120 ✓ and 5(80)+15(40)=400+600=10005(80) + 15(40) = 400 + 600 = 1000

💡 Strategic Tip: Ticket problems combine quantity and revenue equations.

**Other choices fail verification.