A school improv club is selling candy bars and boxes of popcorn as a fundraiser. Boxes of popcorn sell for $5, and candy bars sell for $2. The club's goal is to raise at least $500. Due to pre-orders, they know they will sell at least 45 boxes of popcorn.

Question

A school improv club is selling candy bars and boxes of popcorn as a fundraiser. Boxes of popcorn sell for $5, and candy bars sell for $2. The club's goal is to raise at least $500. Due to pre-orders, they know they will sell at least 45 boxes of popcorn.

To represent the situation, the club president defined x as the number of boxes of popcorn and y as the number of candy bars. Then she wrote this system of inequalities:
x≥45
5x+2y≥500
Does the system of inequalities correctly represent the situation?

Answer 1

Yes, the system of inequalities correctly represents the situation. The first inequality x≥45 represents that they will sell at least 45 boxes of popcorn. The second inequality 5x+2y≥500 represents the total amount of money raised from selling popcorn and candy bars should be greater than or equal to $500.