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

Answer:

A system of inequalities to represent this scenario :

$x+y \leq 20000$

$70x+20y\geq 500000$

Step-by-step 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

Solution:

Let x = the number of $70 seats sold

Let y = the number of $20 seats sold

x+y ≤ 20,000

70x+20y > 500,000