Final answer:
The equation to find the number of student and adult tickets sold, with c representing the number of student tickets sold, is 5c + 10(512 - c) = 3,570. This equation uses the ticket prices and total collected amount to calculate the ticket quantities.
Step-by-step explanation:
To find the number of student and adult tickets sold for the school drama performance, we can set up an equation. We're given that student tickets cost $5 each and adult tickets cost $10 each. The total amount collected from the sale of tickets is $3,570, with 512 tickets sold in total.
Let c represent the number of student tickets sold. Since adult tickets are the remaining tickets, the number of adult tickets will be 512 - c. Now we can form an equation based on the total amount collected:
5c + 10(512 - c) = 3,570
This equation accounts for the total value of student tickets sold (5c) plus the total value of adult tickets sold (10 times the number of adult tickets, which is 512 - c) to give us the total amount of money collected, which is $3,570.