Question 330157
Let's call the cola mix C and the lemon lime mix, L.
Think of the glass as being filled with small marbles that are the molecules of cola and lemon lime.
Let's assume there are 5000 C marbles in the left glass and 5000 L marbles in the right. 
We take out 100 L marbles from the right glass leaving 4900 L marbles in the right.
We now have 5100 marbles in the left glass, 5000 C and 100 L marbles. 
We mix those and now take 100 marbles from the left. 
The distribution of C to L should be 5000/5100 and 100/5100 in the 100 marbles we choose or (98 C, 2 L)
When we add them to the right hand side, the right hand side will have 98C and 4902 L marbles.
The left hand side will have (5000-98=) 4902 C and (100-2=) 98 L marbles
The distribution is the same.