Jaymie 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.

To find out in about how many weeks their savings in the bank will be equal, we can calculate the difference in their initial amounts, which is $595.25 - $147.25 = $448.

Then, we find out the difference in their weekly transactions, which is $27.50 - $23.70 = $3.80.
To estimate how many weeks it will take for their savings to be equal, we divide the difference in their initial amounts by the difference in their weekly transactions, which is $448 / $3.80 = 118.
Therefore, the most reasonable estimate is that their savings in the bank will be equal in about 118 weeks. Answer: \boxed{118}.