You and your friend are going to sell popcorn. You have determined that it will cost you $1.50 to make every popcorn and an additional cost of $450 to run your business. If you plan to sell the popcorn for $3.75, write a system of equations to model the situation then determine how many bags of popcorn you must sell to break even.

3.75x = 450 + 1.50x

They should sell 200 bags of popcorn to break even

Step-by-step explanation:

Business Modeling

When modeling the operation of a business, there are some magnitudes that should be managed to properly control the profits of the business. Those magnitudes are Costs, Revenue, and Profits.

The profit is the difference between the costs and the revenue as follows:

P(x) = R(x) - C(x)

Where x is the number of units produced and sold.

The break-even level is the value of x that produces zero profits, i.e.,

R(x) = C(x)

The costs associated to sell popcorn consist of a fixed amount of $450 plus a variable cost of $1.50 for every popcorn. Thus the total cost function is:

C(x) = 450 + 1.50x

The income or revenue is the selling price times the number of popcorns:

R(x) = 3.75x

The break-even level can be calculated by solving the equation:

3.75x = 450 + 1.50x

Solving the equation:

3.75x - 1.50x = 450

2.25x = 450

x = 450/2.25

x = 200

They should sell 200 bags of popcorn to break even

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