11. The drama club is selling tickets to its play. An adult ticket costs $15 and a student ticket
costs $11. The auditorium will seat 300 ticket-holders. The drama club wants to collect at least
$3630 from ticket sales.
a) Write and graph a system of four inequalities
that describes how many of each type of
ticket the club must sell to meet its goal.
15a+11s is greater than or equal to 360
a+s is less than or equal to 300
Student tickets to the Homecoming game cost $5 each. General admission tickets cost $8 each. So far, 150 tickets have been sold. $900 has been collected.
A. Write a system of equations for this model in standard form.
To write a system of inequalities that describes how many adult and student tickets the drama club must sell, we need to consider the following:
Let's assume the number of adult tickets sold as "x" and the number of student tickets sold as "y".
The first inequality we can write is based on the goal of collecting at least $3630 from ticket sales:
15x + 11y ≥ 3630
This inequality ensures that the total revenue from ticket sales is equal to or greater than $3630.
The next three inequalities are based on the seating capacity of the auditorium, which will seat 300 ticket-holders:
1. The total number of tickets sold should not exceed the seating capacity:
x + y ≤ 300
2. The number of adult tickets sold should not exceed the seating capacity:
x ≤ 300
3. The number of student tickets sold should not exceed the seating capacity:
y ≤ 300
By graphing these four inequalities on a coordinate plane, we can visually represent the solution space that satisfies the given conditions. The shaded region on the graph where all four inequalities overlap represents the valid solutions for the number of adult and student tickets to be sold.