Algebraically determine number of tickets sold

Question

. For our class trip, 130 tickets were purchased. The cost of a faculty ticket was $16,500. The cost of a student ticket was 60% of the cost of a faculty ticket. A total of
$ 1,570,800 was collected. Algebraically, determine how many faculty and how many student tickets were sold.

Answer 1

John, let's let x = the number of student tickets and y = the number of faculty tickets.

 

We are given that x + y = 130.

 

The total cost of faculty tickets was 16500y.

 

The word "of" means to multiply, so the total cost of student tickets is .6(16500x) = 9900x, soooo...

 

9900x + 16500y = 1570800

 

We need to solve the first equation for x or y. Let's do x.

 

x = 130 - y

 

Now we plug in y -130 for x in the 2nd equation.

 

      9900(130 - y) + 16500y = 1570800

1287000 - 9900y + 16500y = 1570800

                                     6600y = 283800

                                              y = 43

 

x = 130 - 43 = 87

 

Hope this helps!