A local foundation organized a lunch party for all the kids in the community. They ordered a total of 500 burger meals. They ordered plain burgers at $1.75 each, cheeseburgers at $2.50 each, and chicken burgers at $3.20 each. They ordered mostly cheeseburgers, and 100 fewer chicken burgers than plain burgers. The total order came to $1,172.50. Define the variables and write a system of equations to represent the situation.