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 no more than 75 people. The drama club must make at least $480 from ticket
sales to cover the show's costs. If a 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

Answer:(20, 100).

Explanation:

Formation of inequalities and their solution,

To form an inequality choose the variables.

Point lying in the common region of the inequalities will be the solution of the inequalities.

Given in the question,

Cost of student ticket = $5 each

Cost of adult ticket = $9.5 each

Let the number of student tickets sold = x

And the number of adult tickets sold = y

First statement states," Auditorium can hold a maximum of 130 people".

Inequality for the statement will be,

x + y ≤ 130 --------(1)

Second statement states, "The drama club must make at least $950 from the tickets sale to cover the show's cost".

Inequality for the statement will be,

5x + 9.5y ≥ 950 ------ (2)

Now use the utility to graph the inequality,

Since, a point (20, 100) lies in the common region (solution area) of the inequalities,