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 $9. The auditorium can
hold a maximum of 122 people. The drama club must make no less than $890 from
ticket sales to cover the show's costs. If 45 student tickets were sold, determine the
minimum number of adult tickets that the drama club must sell in order to meet the
show's expenses. If there are no possible solutions, submit an empty answer.
Answer:
A system of equations can be set up to represent the problem:
s = number of student tickets sold
a = number of adult tickets sold
s + a ≤ 122 (maximum number of people who can attend)
5s + 9a ≥ 890 (minimum amount of money needed)
Substitute s = 45 into the second equation and solve for a:
5(45) + 9a ≥ 890
225 + 9a ≥ 890
9a ≥ 665
a ≥ 73.9
Since a must be a whole number, the drama club must sell at least 74 adult tickets to meet the show's expenses.
To determine the minimum number of adult tickets that the drama club must sell, we can start by calculating the money raised from student ticket sales.
Since each student ticket sells for $5 and 45 student tickets were sold, the total money raised from student ticket sales is 45 x $5 = $225.
Next, we need to calculate the remaining amount of money needed to meet the show's expenses.
Since the drama club must make no less than $890 and the money raised from student ticket sales is $225, the remaining amount needed is $890 - $225 = $665.
Now, we can determine the number of adult tickets that need to be sold.
Each adult ticket sells for $9, so the number of adult tickets can be calculated as follows:
Number of adult tickets = Remaining amount needed / Price per adult ticket
Number of adult tickets = $665 / $9 ≈ 73.89
Since the number of adult tickets must be a whole number, we round up to the next whole number.
Therefore, the minimum number of adult tickets that the drama club must sell to meet the show's expenses is 74.