Tickets to a show cost $10.50 for adults and $8.50 for students. A group of friends purchased 15 tickets for $149.50. How many adult tickets were purchased?

x - number of adult tickets

y - number of student tickets

{10.5x + 8.5y = 149.5

{x + y = 15

{x = 15 - y

{10.5(15 - y) + 8.5y = 149.5

{x = 15 - y

{157.5 - 10.5y + 8.5y = 149.5

{x = 15 - y

{-2y = -8

{y = 4

{x = 11

They purchased 11 adult tickets.

11 adult tickets were purchased.

Step-by-step explanation:

Let x represent the number of adult tickets that were purchased.

Let y represent the number of adult tickets that were purchased.

A group of friends purchased 15 tickets. This is expressed as

x + y = 15

Tickets to a show cost $10.50 for adults and $8.50 for students. The total cost of the tickets purchased is

$149.50. This is expressed as

10.5x + 8.5y = 149.5 - - - - - - - - - - - -1

Substituting x = 15 - y into equation 1, it becomes

10.5(15 - y) + 8.5y = 149.5

157.5 - 10.5y + 8.5y = 149.5

- 10.5y + 8.5y = 149.5 - 157.5

- 2y = - 8

y = - 8/ - 2

y = 4

x = 15 - y = 15 - 4

x = 11