Select The Correct Answer.Felix Has $ 1 , 000 \$1,000 $1 , 000 In His Savings Account. He Wants To Purchase A Motorcycle For $ 5 , 000 \$5,000 $5 , 000 . The Seller Has Agreed To Take A Payment Of $ 250 \$250 $250 A Month Without Interest. Felix Saves An Extra

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Introduction

Felix, a diligent saver, has been eyeing a motorcycle that costs $5,000\$5,000. He has $1,000\$1,000 in his savings account and wants to purchase the motorcycle. The seller has agreed to accept a payment of $250\$250 per month without interest. In this scenario, Felix needs to determine how many months it will take him to save enough money to purchase the motorcycle. This problem involves a simple mathematical concept: linear equations.

Understanding the Problem

Felix has $1,000\$1,000 in his savings account and wants to purchase a motorcycle for $5,000\$5,000. The seller has agreed to accept a payment of $250\$250 per month without interest. To find out how many months it will take Felix to save enough money to purchase the motorcycle, we need to set up a linear equation.

Setting Up the Equation

Let's denote the number of months it will take Felix to save enough money to purchase the motorcycle as xx. Since Felix saves $250\$250 per month, the total amount he will save in xx months is 250x250x. Felix already has $1,000\$1,000 in his savings account, so the total amount he needs to save is $5,000\$5,000 - $1,000\$1,000 = $4,000\$4,000. We can set up the equation:

250x=4000250x = 4000

Solving the Equation

To solve for xx, we need to isolate the variable. We can do this by dividing both sides of the equation by 250250:

x=4000250x = \frac{4000}{250}

x=16x = 16

Conclusion

Felix needs to save for $250\$250 per month for 1616 months to purchase the motorcycle. This is a simple example of a linear equation, and it illustrates how mathematical concepts can be applied to real-world problems.

Discussion

This problem can be extended to more complex scenarios, such as:

  • What if the seller offers a discount on the motorcycle price?
  • What if Felix wants to purchase a more expensive motorcycle?
  • What if Felix has a variable income and can't save a fixed amount each month?

These questions can be answered by modifying the equation and solving for the new variable.

Real-World Applications

This problem has real-world applications in finance, economics, and personal finance. For example:

  • A person who wants to buy a house may need to save for a down payment, and the seller may offer a payment plan.
  • A business may need to save for a large purchase, such as a new machine or equipment.
  • An individual may need to save for a retirement fund or a college education.

Conclusion

In conclusion, Felix's motorcycle purchase is a simple example of a linear equation. By setting up and solving the equation, we can determine how many months it will take Felix to save enough money to purchase the motorcycle. This problem illustrates the importance of mathematical concepts in real-world applications and can be extended to more complex scenarios.

Additional Resources

For more information on linear equations and their applications, please refer to the following resources:

  • Khan Academy: Linear Equations
  • Mathway: Linear Equations
  • Wolfram Alpha: Linear Equations

Final Thoughts

Introduction

In our previous article, we analyzed Felix's motorcycle purchase and determined that he needs to save for $250\$250 per month for 1616 months to purchase the motorcycle. In this article, we will answer some frequently asked questions related to Felix's scenario.

Q&A

Q: What if Felix wants to purchase a more expensive motorcycle?

A: If Felix wants to purchase a more expensive motorcycle, he will need to save for a longer period of time. Let's assume the new motorcycle price is $7,000\$7,000. Felix already has $1,000\$1,000 in his savings account, so he needs to save an additional $6,000\$6,000. Since he saves $250\$250 per month, he will need to save for:

6000250=24\frac{6000}{250} = 24

months.

Q: What if the seller offers a discount on the motorcycle price?

A: If the seller offers a discount on the motorcycle price, Felix will need to save less money. Let's assume the seller offers a discount of $1,000\$1,000, making the new price $4,000\$4,000. Felix already has $1,000\$1,000 in his savings account, so he needs to save an additional $3,000\$3,000. Since he saves $250\$250 per month, he will need to save for:

3000250=12\frac{3000}{250} = 12

months.

Q: What if Felix has a variable income and can't save a fixed amount each month?

A: If Felix has a variable income and can't save a fixed amount each month, he will need to adjust his savings plan accordingly. Let's assume Felix's income varies between $200\$200 and $300\$300 per month. To determine how many months it will take him to save enough money to purchase the motorcycle, we need to calculate the average monthly savings:

$200+$3002=$250\frac{\$200 + \$300}{2} = \$250

Since Felix saves an average of $250\$250 per month, he will need to save for:

4000250=16\frac{4000}{250} = 16

months.

Q: What if Felix wants to purchase a motorcycle with a different payment plan?

A: If Felix wants to purchase a motorcycle with a different payment plan, he will need to adjust his savings plan accordingly. Let's assume the seller offers a payment plan of $500\$500 per month for 88 months. Felix already has $1,000\$1,000 in his savings account, so he needs to save an additional $3,000\$3,000. Since he saves $500\$500 per month for 88 months, he will need to save for:

3000500=6\frac{3000}{500} = 6

months.

Q: What if Felix wants to purchase a motorcycle with a down payment?

A: If Felix wants to purchase a motorcycle with a down payment, he will need to adjust his savings plan accordingly. Let's assume Felix wants to make a down payment of $1,500\$1,500 and then pay the remaining amount in installments. Felix already has $1,000\$1,000 in his savings account, so he needs to save an additional $500\$500 for the down payment. Since he saves $250\$250 per month, he will need to save for:

500250=2\frac{500}{250} = 2

months.

Conclusion

In conclusion, Felix's motorcycle purchase is a simple example of a linear equation. By answering some frequently asked questions related to Felix's scenario, we have demonstrated how mathematical concepts can be applied to real-world problems. Whether Felix wants to purchase a more expensive motorcycle, a motorcycle with a different payment plan, or a motorcycle with a down payment, he will need to adjust his savings plan accordingly.

Additional Resources

For more information on linear equations and their applications, please refer to the following resources:

  • Khan Academy: Linear Equations
  • Mathway: Linear Equations
  • Wolfram Alpha: Linear Equations

Final Thoughts

Felix's motorcycle purchase is a simple example of a linear equation, but it has real-world applications in finance, economics, and personal finance. By understanding and applying mathematical concepts, we can make informed decisions and achieve our goals.