At a school fundraiser, adult tickets cost $5 each and student tickets cost $3 each. Suppose represents the number of adult tickets sold and represents the number of student tickets sold. If 40 tickets were sold in total and $160 was collected, which system of equations represents this situation?
A system of equations is two equations that must both describe the same situation. Two kinds of tickets, a ticket total, and a money total signal one equation for each total. Add the ticket counts; for money, multiply each price by its own ticket count before adding. Swapping the totals mixes tickets and dollars.
Hints
- Hint 1
For the ticket count, each adult ticket and each student ticket contributes one ticket. What sum of and equals the total number sold?
- Hint 2
For the money total, multiply each price in dollars per ticket by the number of that kind of ticket. Which term counts money from adult tickets, and which counts money from student tickets?
Step-by-step
Write one equation for each total
Step 1Count all the tickets
No Desmos needed. You're matching equations to the story, not solving for the ticket counts. Every ticket sold is adult or student, so add and to get the ticket total:
- Step 2
Add the money collected
Each adult ticket costs $5, so adult tickets bring in dollars. Likewise, student tickets bring in dollars. Add those amounts to get the money total:
Keep ticket counts with tickets and dollar amounts with dollars. These two equations form the system that represents the fundraiser. Choice A.