The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $7.50 and each adult ticket sells for $10. The auditorium can hold a maximum of 134 people. The drama club must make a minimum of $1200 from ticket sales to cover the show's costs. If 85 adult tickets were sold, determine all possible values for the number of student tickets that the drama club must sell in order to meet the show's expenses. Answer:

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The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for  $7.50 and each adult ticket sells for  $10. The auditorium can hold a maximum of 134 people. The drama club must make a minimum of  $1200 from ticket sales to cover the show's costs. If 85 adult tickets were sold, determine all possible values for the number of student tickets that the drama club must sell in order to meet the show's expenses. Answer:

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Calculate Total Revenue: First, calculate the total revenue from the adult tickets sold. Since each adult ticket sells for $10 and 85 adult tickets were sold, the total revenue from adult tickets is: 85 tickets × $10 per ticket = $850.Calculate Minimum Revenue: Next, calculate the minimum revenue needed from student tickets to meet the show's expenses. The drama club needs to make a minimum of $1200, and they have already made $850 from adult tickets. $1200 total needed - $850 from adult tickets = $350 needed from student tickets.Determine Number of Student Tickets: Now, determine the number of student tickets that need to be sold to make at least $350. Since each student ticket sells for $7.50, divide the total needed revenue from student tickets by the price per student ticket. $350 needed ÷ $7.50 per student ticket = 46.666... Since you can't sell a fraction of a ticket, the drama club needs to sell at least 47 student tickets to meet the minimum revenue.Check Auditorium Capacity: Finally, check that the total number of tickets sold does not exceed the auditorium's capacity. The auditorium can hold 134 people, and 85 adult tickets have already been sold. 134 total capacity - 85 adult tickets sold = 49 tickets remaining for students.Final Ticket Sales: Since the drama club needs to sell at least 47 student tickets and can sell up to 49 student tickets without exceeding the auditorium's capacity, the possible values for the number of student tickets sold are 47 or 48.

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