Question 330157: Two glasses are each filled half-way with soda. One with cola and the other with lemon-lime. A small amount of the lemon-lime is completely mixed into the cola. The glass is stirred so they are completely mixed. Then the same amount of the mixture is removed from the cola glass and put back into the glass with the lemon-lime. After the exchange, is there more cola in the lemon-lime glass or more lemon-lime in the cola glass?
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! 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.
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