Question

A stadium holds 51,000 seats. Seats sell for $25 in section A, $20 in section B, and $15 in section C. The number of seats in section A equals the total number of seats in sections B and C. If the stadium takes in $1,090,500 from each sold-out event, how many seats does each section hold?

a. Section A: 17,000, Section B: 17,000, Section C: 17,000
b. Section A: 20,000, Section B: 15,500, Section C: 15,500
c. Section A: 17,000, Section B: 17,500, Section C: 16,500
d. Section A: 19,000, Section B: 16,000, Section C: 16,000

Answer 1

By setting up algebraic equations with the given pricing and total revenue information, and knowing that the number of seats in section A is equal to the total seats in B and C combined, we deduce each section has 17,000 seats. Therefore, the correct answer is (a).

Step-by-step explanation:

Calculating Seats Allocation in a Stadium

To solve how many seats each section holds, we need to set up algebraic equations based on the information provided.

We are told that the total revenue from a sold-out event is $1,090,500, and the stadium holds 51,000 seats.

We also know that the number of seats in section A is equal to the total number of seats in section B and C combined. If we let A represent the number of seats in section A, B for section B, and C for section C, we can use the pricing per seat to formulate our equations:

• 
  
• 25A + 20B + 15C = $1,090,500
• 
  
• A = B + C
• 
  
• A + B + C = 51,000

We can substitute the second equation into the first and third equations to find the number of seats in each section. After doing this and solving the system of equations, we find that the correct answer is:

• 
  
• Section A: 17,000
• 
  
• Section B: 17,000
• 
  
• Section C: 17,000

Thus, each section holds 17,000 seats, making option a the correct choice.