How many student tickets and adult tickets were sold?

Question

1. A concert manager counted 600 ticket receipts the day after a concert. The price for a student ticket was $11.50, and the price for an adult ticket was $16.00. The register confirms that $8,925.00 was taken in. How many student tickets and adult tickets were sold?

Answer 1

Define your variables:

 

x=#student tickets

y=#adult tickets

 

Set up your equations:

 

x+y=600  <------This equation represents quantity

11.50x+16y=8925<-------This equation represents cost

 

You can solve via substitution.  I solved the first equation for y:

 

y = 600-x

 

Plug 600-x into the y for the second equation:

 

11.50x + 16(600-x) = 8925

11.50x + 9600-16x = 8925

-4.5x + 9600 = 8925

-4.5x = -675

x = 150

 

To find y, just plug the value you found for x into one of the original equations:

 

x + y = 600

150 + y = 600

y = 450

 

150 student tickets, 450 adult tickets