Rollie was succesful in losing weight he had a goal weight in mind he went on a diet for three months each month he would lose one third of the difference between his current weight and his goal weight and an additional three pounds at the end of three months he was just 3 pounds over his goal weight how many pounds did he lose in those three months? explain

Let's say that in the beginning he weighted x and at the end he weighted x-y, y being the number of kg he wanted to loose.

first month he lost
y/3

then he lost:  
(y-y/3)/3
this is
(2/3y)/3=2/9y
explanation: ((y-y/3) is what he still needed to loose: y minus what he lost already

and then he lost
 (y-2/9y-1/3y)/3+3 (the +3 is his additional 3 pounts)
 (y-2/9y-1/3y)/3-3=(7/9y-3/9y)/3+3=4/27y+3

it's not just y/3 because each month he lost one third of what the needed to loose at the current time, not in totatl

and  the weight at the end of the 3 months was still x-y+3, 3 pounds over his goal weight!

so:  x -y/3-2/9y-4/27y-3=x-y+3

we can subtract x from both sides:
-y/3-2/9y-4/27y-3=-y+3
add everything up:

-19/27y=-y+6

which means
-19/27y=-y+6

y-6=19/27y

8/27y=6
4/27y=3
y=20.25

so... that's how much he wanted to loose, but he lost 3 less than that, so 23.25

ps. i hope I didn't make a mistake in counting, let me know if i did. In any case you know HOW to solve it now, try to do the calculations yourself to see if they're correct!