Context Inequality

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 $7.50. The auditorium can hold no more than 75 people. The drama club must make a minimum of $450 from ticket sales to cover the show's costs. If x represents the number of student tickets sold and y represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.

Answer 1

The first we need to do is write down the equations that represent ticket sales.

5.00x + 7.50y >= 450.00

x + y <= 75

To solve graphically, you need to graph the lines of the two inequalities.

After doing so, all possible combinations of student and adult ticket sales will be in the shaded region of overlap between the two inequalities. At this point, you may randomly pick a point from this region and it will satisfy the question of one possible solution.