. .
Subj:.....Egg-Citing Eggs-Perience (S668)
          From: MathNexus.wwu.edu
          on 11/16/2008
Drawing from MathNexus...

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
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¢.