Question

Your school club is selling popcorn at a football game. The cost of making the popcorn is $90. You charge 1.50 for each bag of popcorn. A.) Write a function you can use to find the profit P for selling B bags of popcorn. B.) You will break even if the cost of making popcorn equals your income. How many bags of popcorn must you sell to break even?

Answer 1

Answers:

A) The profit function is P(x) = 1.50x - 90 where P is the profit and x is the number of bags sold

B) You must sell 60 bags to break even.

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Explanation:

x = number of bags sold

1.50*x = 1.50x = revenue earned from selling x bags at $1.50 a bag

The revenue is the amount of money you earn. The cost is 90 which is subtracted off the revenue to get the profit, so P(x) = 1.50x - 90 is the profit function.

The breakeven point happens when the profit P is 0. Replace P(x) with 0 and solve for x

P(x) = 1.50x - 90

1.50x - 90 = P

1.50x - 90 = 0 ... replace P with 0

1.50x = 90 ... add 90 to both sides

x = 90/1.50 ... divide both sides by 1.50

x = 60

If you sold 60 bags of popcorn, then you will break even. This is where the profit is $0. You do not make any money, nor do you lose any money. If you sell more than 60 bags, then the profit will be some positive number.