Question

Johanna starts the month with $54 in her savings account. At the end of each week, Johanna adds $8 to the account.

a. how much will Johanna have in her account after 5 weeks?

b. write an equation that could be used calculate Johanna's total savings (S) based on how many weeks (w) she has deposited money in the bank.

c. use your equation to determine how many weeks have passed when Johanna reaches $166 in her account. ​

Answer 1

a) $94

b) S = 54 +8w

c) 14 weeks

Explanation:

The initial value of the account and its rate of change are given. These can be used to find the value at a time, or the time to reach a value.

a.

For each of 5 weeks Johanna added $8, so will have added 5×$8 = $40 after 5 weeks. When that is added to the original $54, the balance will be ...

account balance = $54 + $8 × 5

account balance = $54 +40 = $94

b.

Using S for the account balance, and w for the number of weeks, the above equation becomes ...

S = 54 +8w

c.

We can substitute 166 for S in the equation of part b to find the necessary value of w:

166 = 54 +8w

112 = 8w . . . . . . . . subtract 54

14 = w . . . . . . . . divide by 8

14 weeks will have passed when Johanna has $166 in her account.