Counter-Intuitive Cork

Copyright 1995 by Paul Niquette. All rights reserved.
Sophisticated solvers will not be put off by an elementary 'word problem,' for they have discovered that algebra is a language with exceptional power. 

Let B represent the price of the bottle, C the price of the cork. We have that...

    B + C = 1.10 ~~~~~~~~~~~~~~~~~~~~~~~~~~ from the first sentence, and
    B = C + 1.00 ~~~~~~~~~~~~~~~~~~~~~~ from the second sentence, thus
    2 B + C = C + 2.10 ~~~~ by the principle of 'equals added to equals,' and
    2 B = 2.10 ~~~ by the principle of 'equals subtracted from equals,' thus
    B = 1.05 ~~~~ by the principle of 'equals divided by equals,' so then
    C = 0.05 ~~~~~~~~~~~~~~~~ that's a nickel, folks -- not a dime.

Here's a new challenge:
Try making up a problem which relates the prices of all these various liquids. (See Bottle Royal).

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