For a school fundraiser, student tickets cost $5 each and adult tickets cost $8 each. The event collected a total of $1,176 from ticket sales. If 48 more student tickets than adult tickets were sold, which equation can be used to determine the number of adult tickets, , that were sold?
Ticket-sale problems often call for a one-variable equation even when there are two kinds of tickets: a comparison lets you write both counts using one letter. Multiply each count by its own price, then add the money collected from each group to match the total. Keep the prices with the right groups, and check which group has more tickets before adding a difference.
Hints
- Hint 1
The variable counts adult tickets, but there are more student tickets. Start with the adult count and add the extra tickets. What expression gives the student count?
- Hint 2
A rate is a price per ticket. Multiply each price by the number of tickets sold at that price. What are the separate money amounts from adult and student tickets?
- Hint 3
The total revenue is all the money collected from ticket sales. Add the two money amounts, then set that sum equal to the amount the event collected.
Step-by-step
Build the ticket-sales equation
Step 1Write the student ticket count
No Desmos needed. The question asks you to build an equation, not solve it. The variable counts adult tickets. There are 48 more student tickets, so the student count is , not . Add the extra tickets to the group that has more.
- Step 2
Find the money from each group
Multiply each ticket price by its ticket count. Adult tickets bring in dollars, and student tickets bring in dollars. Keep each price with its own group: would charge the adult tickets the student price.
- Step 3
Match the ticket money to the total
The event collected $1,176 altogether, so add the two money amounts and set them equal to the total revenue:
This equation can determine the number of adult tickets, . Choice D.