Question

A theater manager is planning an upcoming concert. Regular tickets will cost $12 and student tickets will cost $8. The theater can seat at most 200 people. The manager wants to collect at least $1000 from ticket sales. Let x represent the number of regular tickets sold. Let y represent the number of student tickets sold. Select all inequalities that represent constraints for this situation.

Answer 1

Let x be the number of regular tickets
Let y be the number of student tickets

At the most, we can seat 200 people (both regular tickets and student tickets holder). So the inequality is given by:
`x+y \leq 200`

One regular ticket cost $12, so
`x` numbers of regular tickets cost
`12x`

One student ticket cost $8, so
`y` numbers of student tickets cost
`8y`

We want to at least get $1000 from the ticket selling, so the inequality is given by:
`12x+8y \geq 1000`

The constraint is given by simplifying both inequalities to the lowest term

First, we have
`x+y \leq 200` ⇒ This is already the lowest term
Second, we have
`12x+8y \geq 1000`
Simplifying this by dividing each term by 4, we have
`3x+2y \geq 250`

The two constraining inequalities are:

`x+y \leq 200`

`3x+2y \geq 250`