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 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?

Part C
Write an expression to represent the net change to Callie’s account balance each month.


Part D
Simplify the expression in part C to find the net change to Callie’s account balance each month.
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

Part F
What is the sign of the net change in part E? Why does the sign make sense in this situation?

Part A The net change to Callie’s bank account is -$416.48. The negative sign indicates money leaving Callie’s account.

Part B Callie has 4 months to pay off the bill. The rational number is +4. The sign is positive because it represents a quantity of something, in this case, months.

Part C The amount of the bill, -$416.48, will be deducted from Callie’s account in equal amounts over 4 months. So, the expression representing the net change in her account balance each month is -416.48/4 .

Part D -416.48/4=104.12

Part E The monthly withdrawal from Callie’s account continues to be -$104.12. After 1 year (12 months), the net change to her account balance will be -$104.12 × 12 = -$1,249.44.

Answer:

part a)

ANSWER: The net change to Callie’s bank account is -$416.48. The negative sign indicates money leaving Callie’s account.

part b)

ANSWER: Callie has 4 months to pay off the bill. The rational number is +4. The sign is positive because it represents a quantity of something, in this case, months.

part c)


ANSWER: The amount of the bill, -$416.48, will be deducted from Callie’s account in equal amounts over 4 months. So, the expression representing the net change in her account balance each month is -416.48/4 .

part d)

ANSWER: -416.48 / 4= -$104.12

part e)

ANSWER: The monthly withdrawal from Callie’s account continues to be -$104.12. After 1 year (12 months), the net change to her account balance will be -$104.12 × 12 = -$1,249.44.

part f)

ANSWER: The net change is -$1,249.44. The sign is negative because it represents money leaving, or being deducted from, Callie’s bank account.


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