Modeling the Cost of Having Appliance Fixers Handle the Repair

Oct 13, 2025 by wbrum.org 107 views

Introduction

In mathematics, functions are used to model real-world situations and relationships. In this scenario, Lionel uses two functions to represent the costs of having a problem diagnosed and repaired by two appliance repair companies. In this article, we will explore how Lionel models the cost of having Phil's Appliances handle the repair.

Understanding the Problem

Lionel wants to compare the costs of having two different appliance repair companies handle a problem. He decides to use functions to model the costs of having Phil's Appliances and another company, let's call it "Appliance Fixers," handle the repair. The cost of having Phil's Appliances handle the repair is represented by the function C(P), where P is the price of the repair. The cost of having Appliance Fixers handle the repair is represented by the function A(P), where P is the price of the repair.

Modeling the Cost of Having Phil's Appliances Handle the Repair

The cost of having Phil's Appliances handle the repair is represented by the function C(P) = 50 + 0.2P. This function represents the fixed cost of having Phil's Appliances handle the repair, which is $50, plus a variable cost of 20% of the price of the repair.

Modeling the Cost of Having Appliance Fixers Handle the Repair

The cost of having Appliance Fixers handle the repair is represented by the function A(P) = 75 + 0.15P. This function represents the fixed cost of having Appliance Fixers handle the repair, which is $75, plus a variable cost of 15% of the price of the repair.

Comparing the Costs

To compare the costs of having Phil's Appliances and Appliance Fixers handle the repair, Lionel needs to select the correct answer from each drop-down menu. The drop-down menus represent the price of the repair, and the correct answer is the one that results in the lowest total cost.

Selecting the Correct Answer

To select the correct answer, Lionel needs to consider the following:

The fixed cost of having Phil's Appliances handle the repair is $50, while the fixed cost of having Appliance Fixers handle the repair is $75.
The variable cost of having Phil's Appliances handle the repair is 20% of the price of the repair, while the variable cost of having Appliance Fixers handle the repair is 15% of the price of the repair.

Using the Functions to Compare the Costs

To compare the costs of having Phil's Appliances and Appliance Fixers handle the repair, Lionel can use the functions C(P) and A(P) to calculate the total cost of each option. For example, if the price of the repair is $100, the total cost of having Phil's Appliances handle the repair is:

C(100) = 50 + 0.2(100) = 50 + 20 = 70

The total cost of having Appliance Fixers handle the repair is:

A(100) = 75 + 0.15(100) = 75 + 15 = 90

Conclusion

In this article, we explored how Lionel uses functions to model the costs of having a problem diagnosed and repaired by two appliance repair companies. We also discussed how to compare the costs of having Phil's Appliances and Appliance Fixers handle the repair by using the functions C(P) and A(P) to calculate the total cost of each option. By selecting the correct answer from each drop-down menu, Lionel can determine which option results in the lowest total cost.

Selecting the Correct Answer from Each Drop-Down Menu

To select the correct answer from each drop-down menu, Lionel needs to consider the following:

The fixed cost of having Phil's Appliances handle the repair is $50, while the fixed cost of having Appliance Fixers handle the repair is $75.
The variable cost of having Phil's Appliances handle the repair is 20% of the price of the repair, while the variable cost of having Appliance Fixers handle the repair is 15% of the price of the repair.

Using the Functions to Compare the Costs

C(100) = 50 + 0.2(100) = 50 + 20 = 70

The total cost of having Appliance Fixers handle the repair is:

A(100) = 75 + 0.15(100) = 75 + 15 = 90

Selecting the Correct Answer

To select the correct answer, Lionel needs to consider the following:

The fixed cost of having Phil's Appliances handle the repair is $50, while the fixed cost of having Appliance Fixers handle the repair is $75.
The variable cost of having Phil's Appliances handle the repair is 20% of the price of the repair, while the variable cost of having Appliance Fixers handle the repair is 15% of the price of the repair.

Conclusion

Selecting the Correct Answer from Each Drop-Down Menu

To select the correct answer from each drop-down menu, Lionel needs to consider the following:

The fixed cost of having Phil's Appliances handle the repair is $50, while the fixed cost of having Appliance Fixers handle the repair is $75.
The variable cost of having Phil's Appliances handle the repair is 20% of the price of the repair, while the variable cost of having Appliance Fixers handle the repair is 15% of the price of the repair.

Using the Functions to Compare the Costs

C(100) = 50 + 0.2(100) = 50 + 20 = 70

The total cost of having Appliance Fixers handle the repair is:

A(100) = 75 + 0.15(100) = 75 + 15 = 90

Selecting the Correct Answer

To select the correct answer, Lionel needs to consider the following:

The fixed cost of having Phil's Appliances handle the repair is $50, while the fixed cost of having Appliance Fixers handle the repair is $75.
The variable cost of having Phil's Appliances handle the repair is 20% of the price of the repair, while the variable cost of having Appliance Fixers handle the repair is 15% of the price of the repair.

Conclusion

Selecting the Correct Answer from Each Drop-Down Menu

To select the correct answer from each drop-down menu, Lionel needs to consider the following:

The fixed cost of having Phil's Appliances handle the repair is $50, while the fixed cost of having Appliance Fixers handle the repair is $75.
The variable cost of having Phil's Appliances handle the repair is 20% of the price of the repair, while the variable cost of having Appliance Fixers handle the repair is 15% of the price of the repair.

Using the Functions to Compare the Costs

C(100) = 50 + 0.2(100) = 50 + 20 = 70

The total cost of having Appliance Fixers handle the repair is:

A(100) = 75 + 0.15(100) = 75 + 15 = 90

Selecting the Correct Answer

To select the correct answer, Lionel needs to consider the following:

The fixed cost of having Phil's Appliances handle the repair is $50, while the fixed cost of having Appliance Fixers handle the repair is $75.
The variable cost of having Phil's Appliances handle the repair is 20% of the price of the repair, while the variable cost of having Appliance Fixers handle the repair is 15% of the price of the repair.

Conclusion

Introduction

In our previous article, we explored how Lionel uses functions to model the costs of having a problem diagnosed and repaired by two appliance repair companies. We also discussed how to compare the costs of having Phil's Appliances and Appliance Fixers handle the repair by using the functions C(P) and A(P) to calculate the total cost of each option. In this article, we will answer some frequently asked questions about modeling repair costs with functions.

Q: What is the purpose of using functions to model repair costs?

A: The purpose of using functions to model repair costs is to represent the relationship between the price of the repair and the total cost of having a problem diagnosed and repaired by an appliance repair company.

Q: How do I determine the fixed cost and variable cost of having an appliance repair company handle the repair?

A: The fixed cost of having an appliance repair company handle the repair is the cost that is incurred regardless of the price of the repair. The variable cost of having an appliance repair company handle the repair is the cost that is incurred based on the price of the repair. For example, if the fixed cost of having Phil's Appliances handle the repair is $50 and the variable cost is 20% of the price of the repair, the total cost of having Phil's Appliances handle the repair is C(P) = 50 + 0.2P.

Q: How do I compare the costs of having different appliance repair companies handle the repair?

A: To compare the costs of having different appliance repair companies handle the repair, you can use the functions C(P) and A(P) to calculate the total cost of each option. For example, if the price of the repair is $100, the total cost of having Phil's Appliances handle the repair is C(100) = 50 + 0.2(100) = 50 + 20 = 70. The total cost of having Appliance Fixers handle the repair is A(100) = 75 + 0.15(100) = 75 + 15 = 90.

Q: What is the significance of the fixed cost and variable cost in modeling repair costs?

A: The fixed cost and variable cost are significant in modeling repair costs because they represent the relationship between the price of the repair and the total cost of having a problem diagnosed and repaired by an appliance repair company. The fixed cost represents the cost that is incurred regardless of the price of the repair, while the variable cost represents the cost that is incurred based on the price of the repair.

Q: How do I determine the correct answer from each drop-down menu?

A: To determine the correct answer from each drop-down menu, you need to consider the fixed cost and variable cost of having each appliance repair company handle the repair. For example, if the fixed cost of having Phil's Appliances handle the repair is $50 and the variable cost is 20% of the price of the repair, the total cost of having Phil's Appliances handle the repair is C(P) = 50 + 0.2P. If the price of the repair is $100, the total cost of having Phil's Appliances handle the repair is C(100) = 50 + 0.2(100) = 50 + 20 = 70.

Q: What is the benefit of using functions to model repair costs?

A: The benefit of using functions to model repair costs is that it allows you to represent the relationship between the price of the repair and the total cost of having a problem diagnosed and repaired by an appliance repair company. This can help you make informed decisions about which appliance repair company to use and how much to budget for the repair.

Conclusion

In this article, we answered some frequently asked questions about modeling repair costs with functions. We discussed the purpose of using functions to model repair costs, how to determine the fixed cost and variable cost of having an appliance repair company handle the repair, and how to compare the costs of having different appliance repair companies handle the repair. We also discussed the significance of the fixed cost and variable cost in modeling repair costs and how to determine the correct answer from each drop-down menu.