A theater sold 900 tickets to a play. Floor seats coast $12 each and balcony seats $10 each. Total receipts were $9,780. How many of each type of ticket were

Question

A theater sold 900 tickets to a play. Floor seats cost $12 each and balcony seats $10 each. Total receipts were $9,780. How many of each type of ticket were sold?

 

Apologies the question did not fit into the question box. 

 

Please show all the work.

 

Thank You!!

Answer 1

Hi Michael

 

For this problem, we are looking at two different kinds of information :  the number of each kind of ticket sold, and the amount of money made on each ticket sold.

First, let x= the number of floor seats sold

y= the number of balcony seats sold

The total number of seats sold is 900, so

x + y = 900

 

That is your first equation.  Now let's think about making money selling tickets.  You have to multiply the number bought by the price per item to get the total.  Floor seats cost $12 each, so the amount they made selling floor seats is 12x.  Balcony seats cost $10 each, so the amount they made selling balcony seats is 10 y.  The total they made is 9780.

12x + 10y = 9780

 

x + y = 900  This looks good for substitution method.

y = 900 - x

 

12x + 10(900 - x) = 9780

12x + 9000 - 10 x = 9780

2x + 9000 = 9780

2x = 780

x = 390

 

y = 900 - 390 = 510

 

CHECK: 12 (390) +10 (510) = 9780