Atheater 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.

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: 

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

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

We want to at least get $1000 from the ticket selling, so the inequality is given by: 

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

First, we have  ⇒ This is already the lowest term
Second, we have 
Simplifying this by dividing each term by 4, we have 

The two constraining inequalities are: