Question

a drama club is selling tickets to the spring musical. the auditorium hold 200 people. tickets cost $12 at the door and $8.50 if purchased in advance. the drama club has a goal of selling at least $1000 worth of tickets to saturday’s show. write a system of inequalities that can be used to model this scenario

Answer 1

As per the problem

The auditorium hold 200 people.

Also the tickets cost $12 at the door and $8.50 if purchased in advance.

The drama club has a goal of selling at least $1000 worth of tickets to Saturday's show.

Let total number of tickets purchased at door be x and the number of tickets purchased in advance be y.

Then revenue for x tickets =12x

Revenue from y tickets=8.50y

Hence the inequality can be set up as below

$x+y\leq 200, \text{ Because the maximum capacity is 200}$

$12x+8.50y\geq 1000$

$x>0,y>0$

Answer 2

12•x+8.50•y>=1,000
x+y=<200

X-number of tickets sold at the door
Y-number of tickets sold in advance