SOLUTION: I am in a problem seminar class and have been asked to answer and prove the following: Two containers, A and B , contain different liquids called a and b correspondingly of equal

Question 68609: I am in a problem seminar class and have been asked to answer and prove the following:
Two containers, A and B , contain different liquids called a and b correspondingly of equal volume. Suppose that one teaspoon of liquid a is poured into container B and then thoroughly mixed. Next suppose that one teaspoon of the uniform mixture in B is poured into container A. Which of the two containers (if any) is more contaminated?
I have tried many different things and I always end up showing that the volumes will then be equal not what the contamination of each is.
Can some one please HELP!!!!!!!
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Suppose there are 100 teaspoons of a liquid and 100 teaspoons
of b liquid to start with
Going step by step, initially you have
100a
100b
-----then move a teaspoon of a to b
100a - 1*a
100b + 1*a
-----then move a teaspoon of b's mixture to a, dividing by 101 to
get 1 teaspoon
------------
100a - 1*a + (100b + 1*a) / (100 + 1)
100b + 1*a - (100b + 1*a) / (100 + 1)
---------now simplify, note that 100b + a is a common factor in the 2nd one
99a + (100/101)b + (1/101)a
(100b + a)(1 - (1/101))
-----------------
(99 + (1/101))a + (100/101)b
(100*(100/101))b + (100/101)a
-----------------
99.0099a + .990099b
99.0099b + .990099a
-----------------
They seem to be equally contaminated with the other
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