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.

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?