A 6000-seat theater has tickets for sale at $27 and $40. How many tickets sold at each price for a sellout performance to generate a total revenue of $181,500?

Question

Really stumped on how to do this one.

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is to set up a system of equations that models the information given to us in the question. On this one we have

x + y = 6000         (since there are 6000 tickets sold in total)

27x + 40y = 181500    (the 27 and 40 are the ticket prices, 181500 is the total revenue)

I would take the first equation and plug in y = 6000 – x into the second equation and solve for x algebraically. When I do that I get that

4500 tickets were sold at $27 and

1500 tickets were sold at $40

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Alright, Roger, I promise it's not that bad.

 

Let x = the number of $27 tickets and let y = the number of $40 tickets.

 

x + y = 6000 (because of the sellout!)

 

27x + 40y = 181,500

 

Now, we can "solve" the first equation for either x or y. Let's do x.

 

x = 6000 - y

 

We substitute this "value" into the 2nd equation.

 

27(6000 - y) + 40y = 181,500.

 

162,000 - 27y + 40y = 181,500

 

13y = 19,500

 

y = 1500

 

Now, let's take that y and plug it in the first equation.

 

x = 6000 - 1500 = 4500

 

Hope this helps!