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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?

User Arne Mertz
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1 Answer

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Answer:

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.

User Dradd
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