Question

Tickets to a concert cost $70, or $20 with a student discount. Ticket sales must exceed $500,000 for the group to perform. If 20,000 seats are available, how many of each type must be sold? Write a system of inequalities to represent this scenario.  Label the variables. Do not solve.

Answer 1

A system of inequalities to represent this scenario :

`x+y \leq 20000`

`70x+20y\geq 500000`

Explanation:

Let x be the no. of normal ticket sold

Let y be the no. of tickets sold with student discount

We are given that 20,000 seats are available

So,
`x+y \leq 20000`

Cost of normal ticket = $70

Cost of x normal tickets = 70x

Cost of student discount ticket = $20

Cost of y normal tickets = 20y

We are given that Ticket sales must exceed $500,000

So,
`70x+20y\geq 500000`

A system of inequalities to represent this scenario :

`x+y \leq 20000`

`70x+20y\geq 500000`

Answer 2

Let x = the number of $70 seats sold

Let y = the number of $20 seats sold

x+y ≤ 20,000

70x+20y > 500,000