Select The Correct Answer From Each Drop-down Menu.Mrs. James Is Planning To Purchase One Of Two Household Appliance Contracts. Company A Offers A Repair Contract That Covers An Unlimited Number Of Repairs For $$ 12.99$ Per Month. Company B
Introduction
When making a decision, it's essential to consider all the available options and their associated costs. In this scenario, Mrs. James is faced with a choice between two household appliance contracts offered by Company A and Company B. The contracts differ in their pricing structure, and it's crucial to analyze the costs to determine which one is more beneficial for Mrs. James. In this article, we will delve into the mathematical analysis of the contracts and help Mrs. James make an informed decision.
Understanding the Contracts
Company A Contract
Company A offers a repair contract that covers an unlimited number of repairs for $12.99 per month. This means that Mrs. James will pay a fixed amount of $12.99 every month, regardless of the number of repairs she needs.
Company B Contract
Company B, on the other hand, offers a contract with a fixed cost of $9.99 per month, plus an additional $29.99 for each repair. This means that Mrs. James will pay a fixed amount of $9.99 every month, and an additional $29.99 for each repair she needs.
Mathematical Analysis
To determine which contract is more beneficial for Mrs. James, we need to analyze the costs associated with each contract. Let's assume that Mrs. James needs to repair her appliances a certain number of times, denoted by the variable x.
Company A Contract
The total cost of the Company A contract can be calculated as follows:
Total Cost = Monthly Fee + Number of Repairs * Cost per Repair = $12.99 + x * $0 (since the cost per repair is $0)
Since the cost per repair is $0, the total cost of the Company A contract is simply the monthly fee of $12.99.
Company B Contract
The total cost of the Company B contract can be calculated as follows:
Total Cost = Monthly Fee + Number of Repairs * Cost per Repair = $9.99 + x * $29.99
The total cost of the Company B contract is the sum of the monthly fee and the cost per repair multiplied by the number of repairs.
Comparing the Contracts
To compare the two contracts, we need to determine which one is more cost-effective for Mrs. James. Let's assume that Mrs. James needs to repair her appliances x times.
Company A Contract
The total cost of the Company A contract is $12.99, regardless of the number of repairs.
Company B Contract
The total cost of the Company B contract is $9.99 + $29.99x.
To determine which contract is more cost-effective, we need to compare the total costs of the two contracts.
Break-Even Analysis
To determine the break-even point, we need to find the number of repairs at which the total cost of the Company B contract equals the total cost of the Company A contract.
Let's set up an equation to represent the break-even point:
$9.99 + $29.99x = $12.99
Subtracting $9.99 from both sides gives:
$29.99x = $3.00
Dividing both sides by $29.99 gives:
x = 0.1
This means that if Mrs. James needs to repair her appliances 0.1 times (or 1 time), the total cost of the Company B contract will equal the total cost of the Company A contract.
Conclusion
In conclusion, the mathematical analysis of the household appliance contracts offered by Company A and Company B reveals that the Company A contract is more cost-effective for Mrs. James, regardless of the number of repairs she needs. The Company A contract has a fixed monthly fee of $12.99, while the Company B contract has a fixed monthly fee of $9.99 plus an additional $29.99 for each repair. The break-even analysis shows that if Mrs. James needs to repair her appliances 0.1 times (or 1 time), the total cost of the Company B contract will equal the total cost of the Company A contract.
Recommendation
Based on the mathematical analysis, we recommend that Mrs. James choose the Company A contract, which offers an unlimited number of repairs for $12.99 per month. This contract provides more value for money, especially if Mrs. James needs to repair her appliances frequently.
Final Thoughts
Q: What is the main difference between the two contracts offered by Company A and Company B?
A: The main difference between the two contracts is the pricing structure. Company A offers a repair contract that covers an unlimited number of repairs for $12.99 per month, while Company B offers a contract with a fixed cost of $9.99 per month, plus an additional $29.99 for each repair.
Q: How many repairs can I make with the Company A contract?
A: With the Company A contract, you can make an unlimited number of repairs for $12.99 per month. This means that you can repair your appliances as many times as you need without incurring any additional costs.
Q: What is the cost per repair with the Company B contract?
A: The cost per repair with the Company B contract is $29.99. This means that for each repair you need, you will be charged an additional $29.99 on top of the monthly fee of $9.99.
Q: When is the break-even point for the two contracts?
A: The break-even point for the two contracts is when the total cost of the Company B contract equals the total cost of the Company A contract. Based on our analysis, this occurs when you need to repair your appliances 0.1 times (or 1 time).
Q: Which contract is more cost-effective for me?
A: Based on our analysis, the Company A contract is more cost-effective for you, regardless of the number of repairs you need. This is because the Company A contract has a fixed monthly fee of $12.99, while the Company B contract has a fixed monthly fee of $9.99 plus an additional $29.99 for each repair.
Q: Can I cancel my contract with either Company A or Company B?
A: We recommend that you review the terms and conditions of each contract before signing up. Both Company A and Company B may have cancellation policies in place, so it's essential to understand the terms of your contract before making a decision.
Q: What happens if I need to repair my appliances more frequently than expected?
A: If you need to repair your appliances more frequently than expected, the Company A contract may be more beneficial for you. This is because the Company A contract has a fixed monthly fee of $12.99, which covers an unlimited number of repairs. In contrast, the Company B contract has a fixed monthly fee of $9.99 plus an additional $29.99 for each repair, which may add up quickly if you need to repair your appliances frequently.
Q: Can I switch from one contract to another if I change my mind?
A: We recommend that you review the terms and conditions of each contract before signing up. Both Company A and Company B may have policies in place for switching contracts, so it's essential to understand the terms of your contract before making a decision.
Q: What is the best way to determine which contract is right for me?
A: The best way to determine which contract is right for you is to analyze your needs and budget. Consider how often you need to repair your appliances and how much you are willing to pay for each repair. Based on our analysis, the Company A contract may be more beneficial for you if you need to repair your appliances frequently, while the Company B contract may be more beneficial if you only need to repair your appliances occasionally.