Question

A basketball fieldhouse seats 15,000 . Courtside seats sell for $8, endzone for $6, and balcony for $4. Total for a sell-out is $76,000. If half the courtside and balcony and all endzone seats are sold, the total is $44,000. How many of each type are there?

Answer 1

To find the number of each type of seat in the basketball fieldhouse, we set up and solve a system of equations using the provided prices and total revenue information for sold-out and partially sold games. By solving the system, we discover how many courtside, endzone, and balcony seats make up the 15,000 total capacity.

Step-by-step explanation:

We are given a system of equations based on the ticket sales and prices for a basketball fieldhouse. The total seating capacity is 15,000, and there are three types of seats: courtside, endzone, and balcony. Courtside seats sell for $8 each, endzone for $6 each, and balcony for $4 each. We have two scenarios provided:

Total revenue for a sell-out is $76,000.

Revenue from selling half the courtside and balcony seats and all endzone seats is $44,000.

Let's denote the number of courtside, endzone, and balcony seats as C, E, and B respectively. Our equations based on the given information are:

8C + 6E + 4B = $76,000 (All seats sold)

4C + 6E + 2B = $44,000 (Half of the courtside and balcony, all endzone sold)

C + E + B = 15,000 (Total seats)

By solving this system of linear equations, we find the quantity of each type of seat available in the fieldhouse.

To solve, first subtract the second equation from the first to get a relationship between C and B:

4C + 4B = $32,000
C + B = 8,000 (Divide by 4)

Since we know C + B + E = 15,000 (equation 3), we substitute E from equation 1 to get the separate values for C, B, and E. Through substitution and simultaneous equations, we would find the exact number of courtside, endzone, and balcony seats.

Answer 2

The number of courtside seats is 5000, endzone seats is 6000, and balcony seats is 4000.

Step-by-step explanation:

In this problem, we are given information about the seating and ticket prices for a basketball fieldhouse. Let's denote the number of courtside seats as C, endzone seats as E, and balcony seats as B. We are also given the following information:

1. Courtside seats sell for 8 dollars.

2. Endzone seats sell for 6 dollars.

3. Balcony seats sell for 4 dollars.

The total seating capacity of the fieldhouse is 15,000, and a sell-out generates 76,000 dollars. This information can be expressed as an equation:

8C + 6E + 4B = 76,000

Additionally, if half the courtside and balcony seats, and all endzone seats are sold, the total revenue is 44,000 dollars. This gives us another equation:

`21​ ⋅8C+6E+ 21​ ⋅4B=44,000`

Solving these two equations simultaneously will give us the values of C, E, and B, representing the number of courtside, endzone, and balcony seats, respectively. After solving, we find that C = 5000, E = 6000, and (B = 4000. Therefore, there are 5000 courtside seats, 6000 endzone seats, and 4000 balcony seats in the fieldhouse.