Ann the $198 more than her sister. after their mother gave ann $20 and her sister $60, ann had twice as much as her sister. how much money did ann have at first?
it's easy for people that know algebra!

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

These techniques for elimination are preferred for 3rd order systems and higher. They use "Row-Reduction" techniques/pivoting and many subtle math tricks to reduce a matrix to either a solvable form or perhaps provide an inverse of a matrix (A-1)of linear equation AX=b. Solving systems of linear equations (n>2) by elimination is a topic unto itself and is the preferred method. As the system of equations increases, the "condition" of a matrix becomes extremely important. Some of this may sound completely alien to you. Don't worry about these topics until Linear Algebra when systems of linear equations (Rank 'n') become larger than 2.