Suppose a vendor sells seat tickets and floor tickets to a concert. She would like to determine the price she should charge for each ticket type to meet her needs. She can admit 500 people on the floor and 250 people for seats. She needs a concert revenue of $25,750 in order to cover her costs and to take home a little bit of profit. Additionally, the average of the two ticket prices should be $20 so that the average price that shows up on her website sounds appealing to concert-goers. Assume she will fill up the venue.
1. Set up the problem above as a system of linear equations problem. Clearly explain your thought-process. Solve the system and analyze the results. Incorporate a graph of your solution. If any issues exist with the solution, discuss what happened and why it happened.