Algebra Challenge: The Theater's Seating Plan
A large theater is selling three types of tickets for a special event:
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Standard seats cost $30 per ticket.
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VIP seats cost $50 per ticket.
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Balcony seats cost $80 per ticket.
In total, 1,200 tickets were sold, and the theater made $50,000 from ticket sales. There were twice as many VIP seats sold as balcony seats.
Using x to represent the number of standard tickets sold, y for VIP tickets, and z for balcony tickets, set up a system of equations and solve for x, y, and z.
Hints:
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One equation should represent the total number of tickets sold.
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Another equation should represent the total revenue generated.
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The third equation should reflect the relationship between VIP and balcony seats.
