Suppose you have $28.00 in your bank account and start saving $18.25 every week. your friend has $161.00 in his account and is withdrawing $15 every week. when will your account balance be the same?

28 + 18.25x = 161 -15x (here, x stands for every week this addition or withdrawal happens)

So:
28+18.25x = 161 - 15x
18.25x = 161 - 28 - 15x
18.25x = 133 - 15x
18.25x + 15x = 133
33.25x = 133
x = 133/33.25
x = 4

So, they will have the same balance in 4 weeks. 

If i'm correct the answer is $15.97

The first option would be correct if it were one half and not one