Answer: 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
