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Suppose you have two buckets with equal quantities of oil, but one contains mineral oil and the other synthetic.
You transfer a cup of mineral oil from the mineral bucket to the synthetic bucket. You mix it completely. Then you transfer a cup of the mineral/synthetic mixture back to the mineral bucket. Is there more synthetic in the mineral or more mineral oil in the synthetic?
In other words, is there more synthetic oil in the mineral bucket than there is mineral oil in the synthetic bucket or visa versa? (this isn't a trick question, but feel free to state your assumptions if you want to make any)
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__________________ 2004 silver base 6MT (02-441 5-point harness high-back booster)
ok both buckets have 10 cups of oil. you take one cup out mix it with the synthetic now you have 9 cups of mineral oil in the Mineral bucket and 11 cups of 1/11 mineral/synthetic oil in the other. You take one cup of the 10/11 synthetic 1/11 mineral oil and put it in the mineral oil bucket and you have the following
in the synthetic bucket you have (10/11)*10 cups of synthetic oil and (1/11)*10 cups of mineral oil (10/11M)
in the mineral oil bucket you have 9 and 1/11 cups of mineral and 10/11 cups of synthetic.
so you have the same amount of foreign substance in each bucket
At the start you have X mineral and X synthentic.
In each bucket you have X oil.
At the end you still have X mineral and X synthetic oil,and X oil in each bucket, so it's not possible to have more mineral oil in one bucket than synthetic in the other bucket unless one bucket has more oil than the other bucket.
xr2, that's a really simple way of looking at it that I never thought of... thanks!
Anyway, I really like this problem, even though MazdaspeedFeras got the answer in post #2! (tsk tsk... I guess this one is too easy).
To me the intuitive response is that you'll have more mineral in the synthetic bucket since you transfer pure mineral into the synthetic (while transferring only a a diluted solution back to the mineral bucket). But as well all agree, they are even.
I know a couple more puzzles, but they're too easy... I'll see if I can come up with another one by tomorrow.