Source:
http://mathnexus.wwu.edu/Archive/problem/detail.asp?ID=144
A woman went to a
local outdoor market with 20 eggs,
another woman went
with 30 eggs, and a third woman
went with 50 eggs.
All three women sold their eggs
at the same rate
and received the same amount of money.
How could this be?
.
.


Drawing
from tom on 8/21/2009 
.
.
Note: M.N. (Bellingham)
has already submitted the
clever solution of
"0 eggs/hr. (if the rate is time)
or $0/egg (rate is
cost per egg)." So, let's remove
that possibility
and assume that the rate exceeded
the infamous value
of 0.
Hint: When thinking
in terms of a rate, think in terms
of both "dozen eggs"
and "single eggs."
.
.


Finger pointing down
from darrell94590 on 1/2/2006 
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From: lubin100@ on 4/2/2009 
..
THE SOLUTION
Solution Commentary:
First, a note from the teacher
(H.V.) who submitted
this problem: Different students
will attack this
problem in different ways. Although
a formula may exist
for solving this problem, I would
be willing to bet
most students trying this problem
wouldn't know the
formula. Some may look for a formula,
others may just use
trial and error, while others may
be more systematic.
They may attempt to solve this
problem by dividing
the different groups into an equal
number of sets, which
would put them on the right track
since the dozen eggs
and single eggs are the key. Some
may also interpret
the "same rate" as determined by the
number of eggs they
start out with, instead of charging
the same prices,
and go at it from that angle.
The eggs were sold
at the following rate: Ten cents for
each even dozen and
five cents for each single egg beyond
the even dozen. Thus,
each woman received fifty cents for
her eggs.
Thus 20 eggs = 1 dozen
+ 8 singles = 1(10) + 8(5) = 50¢.
30 eggs = 2 dozen + 6 singles = 2(10) + 6(5) = 50¢.
and 50 eggs
= 4 dozen + 2 singles = 4(10) + 2(5) = 50¢. 