Edward along with his buddies bought caramel popcorn or $4 per bag and buttered popcorn for $1 per bag at a high school football game. They spent a total of $ 35 to buy a total of 17 bags of popcorn.

Part A: Write a system of equations that can be solved to find the number of bags of caramel popcorn and the number of bags of buttered popcorn that they bought at the game. Define the variables used in the equations. (5 points)

Part B: How many bags of caramel popcorn did they buy? How many bags of buttered popcorn did they buy? Explain how you got the answer and why you selected a particular method to get the answer. (5 points)