Posted by Zach on Tuesday, May 4, 2010 at 11:57pm.
A large tank contains 400kg mixture of water and alcohol. The mixture is 64% alcohol by weight. At each step, 100 kg of the mixture will be drained from the tank, replaced with 100 kg of water and then stirred. After three steps, what percent of the final solution will be alchohol?
thanks
~zach

Math  Reiny, Wednesday, May 5, 2010 at 7:20am
At the start we had >64(400) kg of alcohol
100 kg were removed,
so we had .64(300) left, adding 100 kg of water does not change that, so
after 1st step, alcohol left is .64(300) of the 400 kg
in the 2nd step the same argument can be applied
so the amount of alcohol left is .64(.64(300))
after the 3rd step, amount left is .64(.64(.64(300)))
= 300(.64)^3 = 78.64 kg
so the percentage of the tank that is alcohol is 78.64/400 = 19.66%

Math  Zach, Wednesday, May 5, 2010 at 10:08pm
Thank you
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