Question

A theater sold 1,125 tickets for a musical performance. The orchestra seats cost $40 each and the balcony seats cost $25 each. The theater collected $39,000 in ticket sales for the performance. How many orchestra tickets were sold?

Answer 1

725 orchestra seats.

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:
`x+y=1125...(1)`.

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:
`40x+25y=39,000...(2)`.

We will use substitution method to solve our system of equations. From equation (1) we will get,

`y=1125-x`

Substituting
`y=1125-x` in equation (2) we will get,

`40x+25*(1125-x)=39,000`

`40x+28125-25x=39,000`

`15x=39,000-28125`

`15x=10875`

`x=(10875)/(15)`

`x=725`

Therefore, 725 orchestra seats were sold for the musical performance.