Final answer:
By creating a system of linear equations based on the total number of tickets and the total sales, we can use the elimination method to find that Marc sold 241 adult tickets.
Step-by-step explanation:
The question requires us to solve a system of linear equations where we have two variables representing the number of student tickets and adult tickets sold. Marc sold a total of 461 tickets for the school play, and the sales totaled $1624. Student tickets cost $3 each, and adult tickets cost $4 each. To find out how many adult tickets were sold, we'll denote the number of student tickets as 's' and the number of adult tickets as 'a'.
Step 1: Write the equations based on given information
- The total number of tickets sold is 461: s + a = 461
- The total sales from these tickets is $1624: 3s + 4a = 1624
Step 2: Solve the system of equations
You can use substitution or elimination method. In this case, we will use the elimination method to solve for 'a'.
- Multiply the first equation by 3, which gives us: 3s + 3a = 1383
- Subtract it from the second equation: (3s + 4a) - (3s + 3a) = 1624 - 1383, which simplifies to a = 241
So, Marc sold 241 adult tickets.