Question

Mathematics

Nguyen has opened a new bake shop in town selling pies. Nguyen sells each pie for and has spent on rent and maintenance this month. How many pies did Nguyen sell if he made profit this month?

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Best Answer

Let be the number of pies Nguyen sold.

The revenue from selling pies is the product of the price per pie and the number of pies:

Revenue

The cost of selling pies is the sum of the fixed costs (rent and maintenance) and the cost per pie (which we don’t know):

Cost

where is the cost per pie.

The profit for selling pies is:

Profit

We know that Nguyen made a profit of , so we can set up the equation:

Solving for using the information given in the problem:

Plugging this expression for back into the equation:

Multiplying both sides by to eliminate the fraction:

Simplifying:

We can solve for using the quadratic formula:

Simplifying:

The positive root gives the number of pies that Nguyen sold:

Rounding down since Nguyen can’t sell a fraction of a pie, he sold pies.

The revenue from selling

Revenue

The cost of selling

Cost

where

The profit for selling

Profit

We know that Nguyen made a profit of

Solving for

Plugging this expression for

Multiplying both sides by

Simplifying:

We can solve for

Simplifying:

The positive root gives the number of pies that Nguyen sold:

Rounding down since Nguyen can’t sell a fraction of a pie, he sold