Question

A certain concert venue has a total of 500 seats, some of which are premium seats near the stage, with the rest of the seats being standard seats further away from the stage. Premium seats at this venue cost $30, while standard seats at this venue cost $21. At the last concert, a total of $11,616 was collected in seat revenue. Assuming all 500 seats were filled, how many of each type of seat was purchased?

A) 384 premium seats and 116 standard seats
B) 200 premium seats and 300 standard seats
C) 250 premium seats and 250 standard seats
D) 275 premium seats and 225 standard seats

Answer 1

By setting up a system of equations and using elimination, we find that there were 124 premium seats and 376 standard seats sold. The total number of seats is 500, and the revenue from the concert was $11,616.

Step-by-step explanation:

To determine how many premium and standard seats were sold, we can set up a system of equations based on the information provided. Let's denote the number of premium seats as P and the number of standard seats as S. We are given that the total seats in the venue is 500 and that the total revenue from selling all the seats is $11,616, with premium seats costing $30 each and standard seats costing $21 each.

The system of equations based on the given information is:

1. P + S = 500 (total number of seats)
2. 30P + 21S = 11616 (total revenue from seats)

To solve for P and S, we can use either substitution or elimination. If we use elimination, we could multiply the first equation by -21 to set up for elimination of variable S:

• -21P - 21S = -10500
• 30P + 21S = 11616

Adding the two equations gives us 9P = 1116, which leads to P = 124. Substituting P = 124 into the first equation (P + S = 500) gives S = 500 - 124 = 376. Therefore, there were 124 premium seats and 376 standard seats sold.