Final answer:
The drama club sold 45 adult tickets and 85 student tickets. The system of equations based on the total earnings and the number of tickets sold was used to find the number of each ticket type sold.
Step-by-step explanation:
The student's question is about solving a system of equations to determine the number of adult and student tickets sold by the drama club. Given that the club earned $1355 from ticket sales and that adult tickets cost $15 and student tickets cost $8, with a total of 130 tickets sold, we can set up the following equations:
- Let A be the number of adult tickets sold and S be the number of student tickets sold.
- For total amount earned: 15A + 8S = 1355
- For total tickets sold: A + S = 130
To solve the system, we can use substitution or elimination. Firstly, from the second equation, we express A as A = 130 - S and substitute this into the first equation:
15(130 - S) + 8S = 1355
Solving for S gives us the amount of student tickets sold:
1950 - 15S + 8S = 1355
-7S = -595
S = 85
Substituting S = 85 back into the equation A + S = 130, we find that:
A = 130 - 85
A = 45
Therefore, the drama club sold 45 adult tickets and 85 student tickets.