Respuesta :
Answer:
725 orchestra seats.
Step-by-step explanation:
Let x be the number of orchestra seats and y be the number of balcony seats.
It has been given that the theater sold 1,125 tickets for a musical performance. We can represent this information as: [tex]x+y=1125...(1)[/tex].
Given: The cost of each orchestra seat is $40 and the balcony seats cost $25 each. The theater collected $39,000 in ticket sales for the performance.
We can represent this information as: [tex]40x+25y=39,000...(2)[/tex].
We will use substitution method to solve our system of equations. From equation (1) we will get,
[tex]y=1125-x[/tex]
Substituting [tex]y=1125-x[/tex] in equation (2) we will get,
[tex]40x+25*(1125-x)=39,000[/tex]
[tex]40x+28125-25x=39,000[/tex]
[tex]15x=39,000-28125[/tex]
[tex]15x=10875[/tex]
[tex]x=\frac{10875}{15}[/tex]
[tex]x=725[/tex]
Therefore, 725 orchestra seats were sold for the musical performance.
