Question

The drama club is selling tickets to their play to raise money for the show's expenses. each student ticket sells for $5 and each adult ticket sells for $8. the auditorium can hold a maximum of 122 people. the drama club must make no less than $790 from ticket sales to cover the show's costs. if 69 student tickets were sold, determine all possible values for the number of adult tickets that the drama club must sell in order to meet the show's expenses.

Answer 1

To meet the show's expenses, the drama club must sell at least 56 adult tickets.

Step-by-step explanation:

To determine the number of adult tickets the drama club must sell in order to meet the show's expenses, we need to find the remaining amount that needs to be raised after selling the student tickets. We know that the drama club must make no less than $790 from ticket sales, and 69 student tickets have been sold at $5 each, which amounts to $345. So, the drama club needs to raise $790 - $345 = $445 from adult ticket sales.

Now, let's consider the cost of each adult ticket, which is $8. To find the number of adult tickets that need to be sold, we divide the total amount that needs to be raised by the cost of each adult ticket: $445 ÷ $8 = 55.625.

Since we cannot sell a fraction of a ticket, we need to round up to the nearest whole number. Therefore, the drama club must sell at least 56 adult tickets in order to meet the show's expenses.

Answer 2

The drama club must sell at least 56 adult tickets in order to meet the show's expenses.

To determine the number of adult tickets the drama club must sell in order to meet the show's expenses, we can use algebra to solve the problem.

Let's assume that the number of adult tickets sold is represented by the variable 'a'.

We know that each student ticket sells for $5 and each adult ticket sells for $8.

So, the total revenue from student tickets is given by the equation:
Revenue from student tickets = number of student tickets * price per student ticket
Revenue from student tickets = 69 * 5 = $345

The total revenue from adult tickets is given by the equation:
Revenue from adult tickets = number of adult tickets * price per adult ticket
Revenue from adult tickets = a * 8 = 8a

The total revenue from ticket sales must be at least $790 to cover the show's costs.

So, the total revenue from ticket sales is given by the equation:
Total revenue = Revenue from student tickets + Revenue from adult tickets
Total revenue = 345 + 8a

We can now set up an equation to find the value of 'a':
345 + 8a ≥ 790

To solve this inequality, we can subtract 345 from both sides:
8a ≥ 790 - 345
8a ≥ 445

Next, divide both sides by 8:
a ≥ 445/8
a ≥ 55.625

Since we cannot have a fraction of a ticket, we need to round up to the nearest whole number.