Answer:
Pavilion seats: 1000
Lawn seats: 600
Step-by-step explanation:
Let p represent tickets for pavilion seats and l represent that of lawn seats
Then the total number of tickets is
[tex]p + l = 1600....(1)[/tex]
The total revenue is
[tex]25p + 15l = 34000....(2)[/tex]
We make p the subject in the first equation:
This implies that:
[tex]p = 1600 - l.....(3)[/tex]
Put equation (3) into equation (2).
This gives us:
[tex]25(1600 - l) + 15l = 34000[/tex]
Expand to get:
[tex]40000 - 25l + 15l = 34000[/tex]
Group similar terms:
[tex] - 25l + 15l = 34000 - 40000[/tex]
Simplify to get
[tex] - 10l = - 6000[/tex]
[tex] \implies \: l = 600[/tex]
Put l=600 into equation (3) to get:
[tex]p = 1600 - 600 = 1000[/tex]
Therefore 1000 pavilion seats and 600 lawn seats were sold.
