Cindy Spent $\$65.25$ On Ingredients For A Blueberry Pie And $\$62.84$ On Ingredients For A Cherry Pie. Each Slice Of Pie Sells For $\$3.50$.Part A:Which Expression Represents Cindy's Profit If She Sells $b$ Slices

Introduction

Cindy, a skilled baker, has spent a significant amount of money on ingredients for two types of pies: blueberry and cherry. She plans to sell each slice of pie for $\$3.50$. In this article, we will explore the expression that represents Cindy's profit if she sells $b$ slices of pie.

Understanding Profit

Profit is the amount of money earned after deducting the cost of production from the revenue generated. In this case, Cindy's profit will be the difference between the revenue from selling $b$ slices of pie and the total cost of producing the pies.

Calculating Revenue

The revenue from selling $b$ slices of pie can be calculated by multiplying the price of each slice ($\$3.50$) by the number of slices sold ($b$).

$$\text{Revenue} = 3.50b$$

Calculating Total Cost

The total cost of producing the pies is the sum of the cost of ingredients for the blueberry pie and the cost of ingredients for the cherry pie.

$$\text{Total Cost} = 65.25 + 62.84 = 128.09$$

Calculating Profit

Cindy's profit can be calculated by subtracting the total cost from the revenue.

$$\text{Profit} = \text{Revenue} - \text{Total Cost}$$

Substituting the expressions for revenue and total cost, we get:

$$\text{Profit} = 3.50b - 128.09$$

Simplifying the Expression

The expression for profit can be simplified by combining like terms.

$$\text{Profit} = 3.50b - 128.09$$

This expression represents Cindy's profit if she sells $b$ slices of pie.

Conclusion

In conclusion, the expression that represents Cindy's profit if she sells $b$ slices of pie is $3.50b - 128.09$. This expression takes into account the revenue generated from selling the pies and the total cost of producing the pies.

Part B: How many slices of pie must Cindy sell to break even?

To break even, Cindy's profit must be equal to zero. We can set up an equation using the expression for profit and solve for $b$.

$$3.50b - 128.09 = 0$$

Adding $128.09$ to both sides of the equation, we get:

$$3.50b = 128.09$$

Dividing both sides of the equation by $3.50$, we get:

$$b = \frac{128.09}{3.50}$$

Simplifying the expression, we get:

$$b = 36.5$$

Since Cindy cannot sell a fraction of a slice of pie, she must sell at least $37$ slices of pie to break even.

Part C: How many slices of pie must Cindy sell to make a profit of $\$100$?

To make a profit of $\$100$, Cindy's profit must be equal to $100$. We can set up an equation using the expression for profit and solve for $b$.

$$3.50b - 128.09 = 100$$

Adding $128.09$ to both sides of the equation, we get:

$$3.50b = 228.09$$

Dividing both sides of the equation by $3.50$, we get:

$$b = \frac{228.09}{3.50}$$

Simplifying the expression, we get:

$$b = 65.2$$

Since Cindy cannot sell a fraction of a slice of pie, she must sell at least $66$ slices of pie to make a profit of $\$100$.

Conclusion

$$$$$$

Introduction

In our previous article, we explored the expression that represents Cindy's profit if she sells $b$ slices of pie. We also calculated how many slices of pie Cindy must sell to break even and make a profit of $\$100$. In this article, we will answer some frequently asked questions about Cindy's profit from selling pies.

Q: What is the formula for Cindy's profit?

A: The formula for Cindy's profit is:

$$\text{Profit} = 3.50b - 128.09$$

Q: How many slices of pie must Cindy sell to break even?

A: To break even, Cindy must sell at least $37$ slices of pie.

Q: How many slices of pie must Cindy sell to make a profit of $\$100$?

A: To make a profit of $\$100$, Cindy must sell at least $66$ slices of pie.

Q: What is the cost of producing each slice of pie?

A: The cost of producing each slice of pie is $\$3.50$.

Q: What is the total cost of producing the pies?

A: The total cost of producing the pies is $\$128.09$.

Q: How can Cindy increase her profit?

A: Cindy can increase her profit by selling more slices of pie or by reducing the cost of producing the pies.

Q: What is the relationship between the number of slices sold and the profit?

A: The number of slices sold is directly proportional to the profit. As the number of slices sold increases, the profit also increases.

Q: Can Cindy sell a fraction of a slice of pie?

A: No, Cindy cannot sell a fraction of a slice of pie. She must sell at least one whole slice of pie.

Q: What is the minimum number of slices Cindy must sell to make a profit?

A: The minimum number of slices Cindy must sell to make a profit is $37$.

Conclusion

In conclusion, we have answered some frequently asked questions about Cindy's profit from selling pies. We hope this article has provided you with a better understanding of the relationship between the number of slices sold and the profit.

Additional Questions

If you have any additional questions about Cindy's profit from selling pies, please feel free to ask. We will do our best to answer your questions and provide you with a better understanding of the topic.

Related Topics

If you are interested in learning more about profit and loss, we recommend checking out the following topics:

• Profit and Loss: Learn about the basics of profit and loss, including the formula for profit and the relationship between profit and loss.
• Break-Even Analysis: Learn how to perform a break-even analysis, including how to calculate the break-even point and how to use the break-even point to make business decisions.
• Cost-Benefit Analysis: Learn how to perform a cost-benefit analysis, including how to calculate the costs and benefits of a business decision and how to use the results to make informed decisions.

We hope this article has provided you with a better understanding of Cindy's profit from selling pies. If you have any additional questions or topics you would like to learn more about, please let us know.