Tim , Carl and lewis had 126 cards. Carl won 3 from Tim , and Lewis lost 2 to Carl. They then found that Tim had twice as many as Carl, and Carl had twice as many as Lewis.
At the end of the game Tim had ....., Carl had....... and Lewis had ........
At the start of the game Tim had ......., Carl had ........ and Lewis had............
At the end of the game the ratio Tim:Carl:Lewis is 4:2:1
So divide 126 by 7 (i.e. 4+2+1) giving 18.
Tim has 18x4 = 72
Carl has 18x2 = 36
Lewis has 18x1 = 18
72+36+18 = 126
That was after Carl won 3 from Tim , and Lewis lost 2 to Carl (to make it easier rephrase that consistently as Carl won 3 from Tim and 2 from Lewis)
So reverse that to give the position at the start of the game:
Tim has 72+3=75
Carl has 36-3-2=31
Lewis has 18+2=20
75+31+20 = 126