Question 68609
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