Question

Josh opened a savings account with $595.25. Every week, she withdraws $27.50 from her account. Steve opened a savings account with $147.25. Every week, he deposits $23.70 into his account. In about how many weeks will their savings in the bank be equal? Choose the most reasonable estimate.

A. 7 weeks
B. 9 weeks
C. 10 weeks
D. 15 weeks

Answer 1

B. ) After 9 weeks their savings in the bank will be equal.

Explanation:

Let us assume after m weeks, their savings in the bank will be equal.

About Josh:

The amount in the savings account initially = $595.25

Amount withdrawn each week = $27.50

So, the amount withdrawn in m weeks = m x ( Amount withdrawn per week)

= m x ( $27.50) = 27.50 m

⇒ Money left in account = Initial money - Money withdrawn in m weeks

= $595.25 - 27.50 m

⇒ After m weeks, money in Josh ' account is: $595.25 - 27.50 m ... (1)

About Steve:

The amount in the savings account initially = $147.25

Amount deposited each week = $23.70

So, the amount deposited in m weeks = m x ( Amount deposited per week)

= m x ( $23.70) = 23.70 m

⇒ Total Money in account = Initial money + Money deposited in m weeks

= $147.25 + 23.70 m

⇒ After m weeks, money in Steve's account is: $147.25 + 23.70 m ... (2)

Also, after m weeks: Money in Josh's account = Money in Steve's account

⇒595.25 - 27.50 m = 147.25 + 23.70 m

or, ⇒595.25 - 147.25 = 23.70 m + 27.50 m

or, 448 = 51. 2 m

or, m = 8.75 ≈ 9 ⇒ m = 9

Hence, after 9 weeks their savings in the bank will be equal.