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Question

An arena that hosts sporting events and concerts has three sections for 3 levels of seating. For a basketball game seats in Section A cost $100, seats in section B cost $50 and seats in section C cost $35. The number of seats in section C equals the number of seats in sections A and B combined. The arena holds 12,000 seats and the game is sold out. If the total revenue from ticket sales is $560,000, determine the number of seats in each section.

Answer 1

A + B + C = 12000

C = A + B

100A + 50B + 35C = 560,000

 

Since C = A + B...

A + B + A + B = 12000

2A + 2B = 12000

A + B = 6000

 

So, there were 6000 C tix sold.

 

100A + 50B + 35(6000) = 560,000

100A + 50B + 210,000 = 560,000

100A + 50B = 350,000

2A + B = 7000 

 

Since A + B = 6000, then B = 6000 - A

 

2A + 6000 - A = 7000

A = 1000

 

There were 1000 A tix sold.

 

B = 6000 - A = 6000 - 1000 = 5000

 

There were 5000 B tix sold.

 

Let's check!

 

A + B + C = 12,000

1000 + 5000 + 6000 = 12000. Check!

 

C = A + B

6000 = 1000 + 5000. Check!

 

100A + 50B + 35C = 560,000

100(1000) + 50(5000) + 35(6000) = 560,000

100,000 + 250,000 + 210, 000 = 560,000

560,000 = 560,000. Check!

 

Hope this helps!