Question
Activity
Callie was billed $416.48 for car repairs. She will pay the service center in 4 equal monthly installments from her bank account. What is the net change in her bank account balance after each monthly payment? Complete the steps below to solve this problem and others like it.
Part A
In terms of the entire bill, which rational number represents the net change to Callie’s bank account? What does the sign on the number mean?
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Submitted!
Hide Sample Answer
The net change to Callie’s bank account is -$416.48. The negative sign indicates money leaving Callie’s account.
Part B
Which rational number represents the number of months that Callie has to pay off the bill? What does the sign on the number mean?
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Part C
Write an expression to represent the net change to Callie’s account balance each month.
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Part D
Simplify the expression in part C to find the net change to Callie’s account balance each month.
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Part E
After paying the car service center in full, Callie realizes that she should start saving money each month for her future. She decides to invest the same monthly amount that she was paying the service center in a retirement fund. If she invests in the retirement fund for one year, what will the net change in her account balance be during that time?
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Part F
What is the sign of the net change in part E? Why does the sign make sense in this situation?
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Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.
Space used (includes formatting): 0 / 30000
Callie was billed $416.48 for car repairs. She will pay the service center in 4 equal monthly installments from her bank account. What is the net change in her bank account balance after each monthly payment? Complete the steps below to solve this problem and others like it.
Part A
In terms of the entire bill, which rational number represents the net change to Callie’s bank account? What does the sign on the number mean?
Space used (includes formatting): 0 / 30000
Submitted!
Hide Sample Answer
The net change to Callie’s bank account is -$416.48. The negative sign indicates money leaving Callie’s account.
Part B
Which rational number represents the number of months that Callie has to pay off the bill? What does the sign on the number mean?
Space used (includes formatting): 0 / 30000
Part C
Write an expression to represent the net change to Callie’s account balance each month.
Space used (includes formatting): 0 / 30000
Part D
Simplify the expression in part C to find the net change to Callie’s account balance each month.
Space used (includes formatting): 0 / 30000
Part E
After paying the car service center in full, Callie realizes that she should start saving money each month for her future. She decides to invest the same monthly amount that she was paying the service center in a retirement fund. If she invests in the retirement fund for one year, what will the net change in her account balance be during that time?
Space used (includes formatting): 0 / 30000
Part F
What is the sign of the net change in part E? Why does the sign make sense in this situation?
Space used (includes formatting): 0 / 30000
Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.
Space used (includes formatting): 0 / 30000
Answers
Answered by
GPT-4o mini
Sure! Let's complete each part step by step.
### Part A
In terms of the entire bill, which rational number represents the net change to Callie’s bank account? What does the sign on the number mean?
**Answer:**
The net change to Callie’s bank account is -$416.48. The negative sign indicates that money is leaving Callie’s account.
---
### Part B
Which rational number represents the number of months that Callie has to pay off the bill? What does the sign on the number mean?
**Answer:**
The rational number that represents the number of months is 4. The sign is positive, which indicates the duration of time over which she will make payments.
---
### Part C
Write an expression to represent the net change to Callie’s account balance each month.
**Answer:**
The expression to represent the net change to Callie’s account balance each month is:
\[
-\frac{416.48}{4}
\]
This shows the negative change (outflow) divided over the number of months.
---
### Part D
Simplify the expression in part C to find the net change to Callie’s account balance each month.
**Answer:**
To simplify:
\[
-\frac{416.48}{4} = -104.12
\]
Thus, the net change to Callie’s account balance each month is -$104.12.
---
### Part E
After paying the car service center in full, Callie realizes that she should start saving money each month for her future. She decides to invest the same monthly amount that she was paying the service center in a retirement fund. If she invests in the retirement fund for one year, what will the net change in her account balance be during that time?
**Answer:**
If she invests -$104.12 each month for a year (12 months), the total net change will be:
\[
-104.12 \times 12 = -1,249.44
\]
Thus, the net change in her account balance during that time will be -$1,249.44.
---
### Part F
What is the sign of the net change in part E? Why does the sign make sense in this situation?
**Answer:**
The sign of the net change in part E is negative (-$1,249.44). This makes sense because the amount is money going out of her account as she is investing in the retirement fund, indicating a decrease in her bank account balance.
---
### Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.
**Self-Assessment:**
I would rate my work a 5. I have clearly explained each part and simplified the expressions correctly. I learned how to break down a problem into manageable steps and how to interpret the meaning of negative numbers in financial contexts. One challenge was ensuring that I correctly calculated the monthly installment and then extrapolated that to a yearly investment.
### Part A
In terms of the entire bill, which rational number represents the net change to Callie’s bank account? What does the sign on the number mean?
**Answer:**
The net change to Callie’s bank account is -$416.48. The negative sign indicates that money is leaving Callie’s account.
---
### Part B
Which rational number represents the number of months that Callie has to pay off the bill? What does the sign on the number mean?
**Answer:**
The rational number that represents the number of months is 4. The sign is positive, which indicates the duration of time over which she will make payments.
---
### Part C
Write an expression to represent the net change to Callie’s account balance each month.
**Answer:**
The expression to represent the net change to Callie’s account balance each month is:
\[
-\frac{416.48}{4}
\]
This shows the negative change (outflow) divided over the number of months.
---
### Part D
Simplify the expression in part C to find the net change to Callie’s account balance each month.
**Answer:**
To simplify:
\[
-\frac{416.48}{4} = -104.12
\]
Thus, the net change to Callie’s account balance each month is -$104.12.
---
### Part E
After paying the car service center in full, Callie realizes that she should start saving money each month for her future. She decides to invest the same monthly amount that she was paying the service center in a retirement fund. If she invests in the retirement fund for one year, what will the net change in her account balance be during that time?
**Answer:**
If she invests -$104.12 each month for a year (12 months), the total net change will be:
\[
-104.12 \times 12 = -1,249.44
\]
Thus, the net change in her account balance during that time will be -$1,249.44.
---
### Part F
What is the sign of the net change in part E? Why does the sign make sense in this situation?
**Answer:**
The sign of the net change in part E is negative (-$1,249.44). This makes sense because the amount is money going out of her account as she is investing in the retirement fund, indicating a decrease in her bank account balance.
---
### Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.
**Self-Assessment:**
I would rate my work a 5. I have clearly explained each part and simplified the expressions correctly. I learned how to break down a problem into manageable steps and how to interpret the meaning of negative numbers in financial contexts. One challenge was ensuring that I correctly calculated the monthly installment and then extrapolated that to a yearly investment.