An equal fee paid by every attendee and a cost paid once point to a linear equation, an equation with one unknown raised only to the first power. Multiply the fee by the number of attendees, then subtract the fixed cost to match the money left. The trap is treating the amount left after paying as the amount originally collected.
Hints
- Hint 1
The total money collected is called revenue. Because each person pays the same fee, multiply one person's fee by the number of attendees. What expression gives the club's revenue?
- Hint 2
The net amount is what remains after a cost is paid. Subtract the one-time rental fee from the revenue, then set that equal to the amount the club had left.
Step-by-step
Model the money left, then solve
Step 1Write the total admission revenue
Let be the admission fee in dollars per person. All 50 attendees paid that same fee, so the revenue, or total money collected, was dollars.
- Step 2
Account for the rental fee
The fixed rental fee is paid once, not once per attendee. Money collected minus a one-time cost equals money left. So the net amount is modeled by:
- Step 3
Find the fee per attendee
Type in Desmos. The subscript in makes it an unknown to find rather than the graph's -axis; tells Desmos to match the two sides. Its regression shows under PARAMETERS. Since is the fee for each attendee, the admission fee was $10. Grid in 10.