Farrah Borrowed $ $155 $ From Her Brother. She Has Already Paid Back $ $15 $. Which Equation Describes The Number Of Months It Will Take To Pay Off The Debt If She Pays $ $35 $ Per Month?A. $ X + 15 + 35 = 155 $B.
Understanding the Problem
Farrah borrowed $155 from her brother and has already paid back $15. She wants to pay off the remaining debt by paying $35 per month. The problem is to find the number of months it will take to pay off the debt.
Breaking Down the Problem
To solve this problem, we need to understand the concept of debt and how it can be paid off. When Farrah borrowed $155 from her brother, she incurred a debt of $155. She has already paid back $15, which means she has reduced her debt by $15. The remaining debt is $155 - $15 = $140.
Formulating the Equation
Let's assume it will take x months to pay off the remaining debt of $140. Since Farrah pays $35 per month, the total amount she will pay in x months is $35x. The equation that describes the situation is:
$35x = 140
Solving the Equation
To solve for x, we need to isolate x on one side of the equation. We can do this by dividing both sides of the equation by 35:
x = 140/35
x = 4
Conclusion
The equation that describes the number of months it will take to pay off the debt is x = 140/35. Solving for x, we get x = 4. This means that it will take Farrah 4 months to pay off the remaining debt of $140 if she pays $35 per month.
Alternative Solutions
Let's examine the alternative solutions provided:
A. x + 15 + 35 = 155
This equation is incorrect because it adds 15 and 35 to x, which is not the correct approach to solving the problem.
B. x + 35 = 140
This equation is also incorrect because it subtracts 35 from x, which is not the correct approach to solving the problem.
Conclusion
In conclusion, the correct equation that describes the number of months it will take to pay off the debt is x = 140/35. Solving for x, we get x = 4. This means that it will take Farrah 4 months to pay off the remaining debt of $140 if she pays $35 per month.
Real-World Applications
This problem has real-world applications in finance and accounting. When individuals or businesses borrow money, they need to pay off the debt in a timely manner to avoid interest charges and penalties. This problem demonstrates how to calculate the number of months it will take to pay off a debt based on the amount borrowed, the amount paid back, and the monthly payment amount.
Mathematical Concepts
This problem involves the following mathematical concepts:
- Debt and interest
- Algebraic equations
- Division
- Fractions
Tips and Tricks
When solving this problem, remember to:
- Understand the concept of debt and how it can be paid off
- Formulate the equation correctly
- Solve for x using division
- Check the solution to ensure it makes sense in the context of the problem
Q&A: Paying Off Debts
Q: What is the main concept behind paying off debts?
A: The main concept behind paying off debts is to reduce the amount owed by making regular payments. In the case of Farrah, she borrowed $155 from her brother and wants to pay off the remaining debt by paying $35 per month.
Q: How do I calculate the number of months it will take to pay off a debt?
A: To calculate the number of months it will take to pay off a debt, you need to divide the remaining debt by the monthly payment amount. In the case of Farrah, the remaining debt is $140 and the monthly payment amount is $35. Therefore, the number of months it will take to pay off the debt is 140/35 = 4.
Q: What if I want to pay off the debt faster?
A: If you want to pay off the debt faster, you can increase the monthly payment amount. For example, if Farrah wants to pay off the debt in 2 months, she can increase her monthly payment amount to $70 (140/2 = 70).
Q: What if I want to pay off the debt slower?
A: If you want to pay off the debt slower, you can decrease the monthly payment amount. For example, if Farrah wants to pay off the debt in 6 months, she can decrease her monthly payment amount to $23.33 (140/6 = 23.33).
Q: Can I use a formula to calculate the number of months it will take to pay off a debt?
A: Yes, you can use the formula:
Number of months = Remaining debt / Monthly payment amount
This formula can be used to calculate the number of months it will take to pay off a debt.
Q: What are some real-world applications of paying off debts?
A: Paying off debts has many real-world applications, including:
- Personal finance: Paying off debts is an important part of personal finance. It can help individuals reduce their financial stress and improve their credit score.
- Business finance: Paying off debts is also important for businesses. It can help businesses reduce their financial stress and improve their cash flow.
- Credit score: Paying off debts can also help improve credit scores. When individuals or businesses pay off their debts, it shows lenders that they are responsible and can manage their finances effectively.
Q: What are some tips for paying off debts?
A: Here are some tips for paying off debts:
- Create a budget: Create a budget that outlines your income and expenses. This can help you identify areas where you can cut back and allocate more money towards debt repayment.
- Prioritize debts: Prioritize your debts by focusing on the ones with the highest interest rates or the smallest balances.
- Increase income: Increase your income by taking on a side job or asking for a raise.
- Decrease expenses: Decrease your expenses by cutting back on non-essential spending.
By following these tips and using the formula to calculate the number of months it will take to pay off a debt, you can pay off your debts and improve your financial situation.