Given:
- There are two glasses each filled with equal amounts of liquid; one is lemon-lime while the other is cola.
- A small portion of the lemon-lime is taken out and mixed thoroughly into the glass of cola.
- A portion of the cola lemon-lime mixture, which is equal to the portion that was taken form the glass of lemon-lime originally, is taken out and poured into the glass with pure lemon-lime.
So:
Is there more lemon-lime in the cola glass, or more cola in the lemon-lime glass?
Answer:
It is the same in each glass.
Here's how I got my answer:
- I visualized the two glasses and the amounts being poured from one to the other.
- If a small amount of lemon-lime is taken out of the glass and mixed into the other then that means that there is "that" much more liquid in the cola glass than what is in the lemon-lime glass.
- If that small amount is "thoroughly mixed" into the cola then I would assume that all of the molecules have spread and diffused evenly throughout.
- If you, then, take out the exact same amount of the cola mixture that you did of the original lemon-lime in the beginning THEN
1st- the cola mixture glass would be back to its original amount of liquid, but it would be missing a portion of cola and a tiny portion of the lemon-lime that was mixed into it
2nd- the little amount that you have taken out would be mostly cola with a small portion of lemon-lime
3rd- the ratios of cola to lemon-lime in the cola mixture glass and the small portion that you have taken out should be exactly the same
- If you take that small portion of the cola mixture that you have and add it to the glass of lemon-lime THEN
1st- the two glass would both be back to their original amounts of liquid
2nd- the lemon-lime glass would be gaining back a tiny portion of the amount that it lost before
3rd- the amount of cola in the lemon-lime glass would be a little bit less than the original amount of lemon-lime that was put in the cola glass
-This means that the actual question becomes: Is the amount of cola taken from the cola mixture equal to, less than, or greater than, the amount of lemon-lime that is left in the cola mixture glass?
-And since the portion of lemon-lime that came OUT of the cola mixture makes the lemon-lime amount in the cola mixture glass less, AND it makes the amount of cola in the lemon-lime glass the SAME amount less.....
We can conclude that the amount of cola in the lemon-lime glass is the exact same as the amount of lemon-lime in the cola glass.
*I hope you can follow my logic. Makes sense to me at least.
Wednesday, February 10, 2010
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