SOLUTION: A Broadway theater was 500 seats, divided into orchestra, main, and balcony seating. Orchestra sells at $80, Main sells at $70, and Balcony sells at $40. If all seats are sold out,

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A Broadway theater was 500 seats, divided into orchestra, main, and balcony seating. Orchestra sells at $80, Main sells at $70, and Balcony sells at $40. If all seats are sold out,      Log On

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Question 159193This question is from textbook Intermediate Algebra
: A Broadway theater was 500 seats, divided into orchestra, main, and balcony seating. Orchestra sells at $80, Main sells at $70, and Balcony sells at $40. If all seats are sold out, and the gross revenue to the theater is $30,900. If all the main and balcony are sold out, and only have the orchestra are sold, the gross revenue is $26,900. How many are there of each kind of seat?This question is from textbook Intermediate Algebra

Answer by stanbon(48568) About Me  (Show Source):
You can put this solution on YOUR website!
A Broadway theater was 500 seats, divided into orchestra, main, and balcony
Quantity Equation: r + m + b = 500
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seating. Orchestra sells at $80, Main sells at $70, and Balcony sells at $40. If all seats are sold out, and the gross revenue to the theater is $30,900.
Value Equation: 80r + 70m + 40b = 30,900
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If all the main and balcony are sold out, and only half the orchestra are sold, the gross revenue is $26,900.
Value equation: (1/2)80r + 70m + 40b = 26,900
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How many are there of each kind of seat?
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Rearrange the three equations and solve the system by any means to get:
r = 100
m = 230
b = 170
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Cheers,
Stan H.