Question

The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4.50 and each adult ticket sells for $7.50. The auditorium can hold a maximum of 150 people. The drama club must make a minimum of $900 from ticket sales to cover the show's costs. If xx represents the number of student tickets sold and yy represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.

Answer 1

The drama club is selling student tickets for $4.50 each and adult tickets for $7.50 each. We can write and solve a system of inequalities to determine one possible solution.

Step-by-step explanation:

The drama club is selling student tickets for $4.50 each and adult tickets for $7.50 each. Let's use variables to represent the number of student tickets sold (xx) and the number of adult tickets sold (yy).

We can write two inequalities to represent the given conditions:

1. The total number of tickets sold must not exceed the maximum capacity of 150 people: xx + yy ≤ 150
2. The total revenue from ticket sales must be at least $900: 4.50xx + 7.50yy ≥ 900

To solve this system of inequalities graphically, we can plot the feasible region on a coordinate plane and find a point within the region as a solution. One possible solution would be xx = 50 and yy = 100, which satisfies both inequalities.