Write a system of inequalities to model this situation.

Question

A charity is selling 500 tickets for a benefit concert. The tickets will be sold for $9 before the day of the concert and $12 on the day of the show. The organizers hope to raise at least $5,700 from ticket sales. Write a system of inequalities to model this situation.

Answer 1

There are 500 tickets; let's denote by x the number of tickets to be sold  for $9, befoe the day of concert  and y the number of tickets for $12 on the day of concert. It is clear that x+y=500. Organizers would like to raise revenue at lleast to $5,700, that is $9x+$12y≥$5,700.

So we have the following:

x+y=500

9x+12y≥5,700.

 

3y≥5700-4500

3y≥1200

y≥400

 

x≥100