The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $5.50 and each adult ticket sells for $9.50. There was a total of $703 in revenue from the sale of 98 total tickets. Write a system of equations that could be used to determine the number of student tickets sold and the number of adult tickets sold. Define the variables that you use to write the system.
Give two systems of equations
Let's define the variables:
Let's call the number of student tickets sold as "S".
Let's call the number of adult tickets sold as "A".
System of Equations 1:
From the problem, we know that each student ticket sells for $5.50. Thus, the revenue from the sale of student tickets can be calculated as 5.50S.
Similarly, each adult ticket sells for $9.50, so the revenue from the sale of adult tickets can be calculated as 9.50A.
The total revenue from the sale of tickets is given as $703.
Therefore, the first equation in the system is: 5.50S + 9.50A = 703.
System of Equations 2:
Since we know the total number of tickets sold is 98, we can write a second equation as the sum of the number of student tickets and the number of adult tickets equaling 98. Therefore, the second equation in the system is: S + A = 98.
System of Equations 1:
5.50S + 9.50A = 703
S + A = 98