Answer:
43 faculty tickets and 87 student tickets
Step-by-step explanation:
Let x be the number of faculty tickets sold and y be the number of student tickets sold.
130 tickets were purchased, so
x + y = 130
The cost of faculty ticket was $16.50, then x tickets cost $16.50x.
The cost of student tickets sold was $9.90, then y tickets cost $9.90y.
A total of $ 1,570.80 was collected, thus
16.50x + 9.90y = 1,570.80
You get the system of two equations:
[tex]\left\{\begin{array}{l}x+y=130\\ \\16.50x+9.90y=1,570.80\end{array}\right.[/tex]
From the first equation:
[tex]x=130-y[/tex]
Substitute it into the second equation:
[tex]16.5(130-y)+9.9y=1,570.8\\ \\165(130-y)+99y=15,708\\ \\55(130-y)+33y=5,236\\ \\7,150-55y+33y=5,236\\ \\-55y+33y=5,236-7,150\\ \\-22y=-1,914\\ \\22y=1,914\\ \\y=87\\ \\x=130-87=43[/tex]
43 faculty tickets and 87 student tickets
