Let us assume the initial money that Ann had = x dollars
Let us assume the initial money that her sister had = y dollars
Amount that Ann had after their mother gave $ 20 = (x + 20) dollars
Amount that her sister had after their mother gave $60 = (y + 60) dollars
Then
x - y = 198
x + 20 = 2(y + 60)
The above two equations can be deduced from the details given in the question.Noe let us take the first equation and deduce the value of y in terms of x
Then
x - y = 198
-y = 198 - x
y = x - 198
Now we will put the value of x in the second equation, we get
x + 20 = 2(y + 60)
x + 20 = 2(x - 198 + 60)
x + 20 = 2x - 396 + 120
x - 2x = 120 - 20 - 396
-x = - 296
x = 296
So the initial amount that Ann had was $296.
x = 496/3
= 165.33 dollars
