Method 1(Trial and error)
Mira 's original amount=$760
Paulina' s original amount=$210
By trial and error method , we have ,
760-40-40-40-40-40=210+70+70+70+70+70 (the number of -40's and 70 's had to be the same or else these 2 would have never had equal amounts of money.)
number of -40's (or 70's) =5
Hence, after 5 months , the former will have the same amount of money as the latter.
Method 2(Algebric method)
Let the number of months after which the amounts of both the girls would be same be x .
Money withdrawn by Mira in x months=40*x=40x
Money deposited by Pauline in x months=70*x=70x
Since the amounts need to be equal,
or,x=550/110 = 5
Hence the required number of months is 5.
(Note that from both the answers , the result is same)