Question

The drama club is selling tickets to their play to raise money for the show's expenses.

Each student ticket sells for $4 and each adult ticket sells for $9. The auditorium can
hold no more than 110 people. The drama club must make a minimum of $720 from
ticket sales to cover the show's costs. If r represents the number of student tickets
sold and y represents the number of adult tickets sold, write and solve a system of , a
inequalities graphically and determine one possible solution.

Answer 1

Answer: The total number of tickets sold (student and adult) cannot exceed 110, so we can write the first inequality as:

r + y ≤ 110

The minimum amount of money needed from ticket sales is $720, so we can write the second inequality as:

4r + 9y ≥ 720

To graph the system of inequalities, we can start by plotting the two lines corresponding to r + y = 110 and 4r + 9y = 720. The solution to the system of inequalities is the area on the graph that is shared by both of the inequalities (i.e., the area above the line 4r + 9y = 720 and below the line r + y = 110).

One possible solution for the number of student tickets (r) and adult tickets (y) is (30, 80). This means that 30 student tickets and 80 adult tickets can be sold to meet the conditions and raise at least $720.

Explanation: