Title
The Salesman and the Eggs
Problem Statement
An egg salesman had his first customer. The customer wanted to buy half of the
salesman's eggs plus half of an egg. His second and third customer wanted the
same thing. He did not have to break any eggs and had no eggs left over when he
was finished. How many eggs did he start with?
Problem setup
We decided we did not have to use the
Excel spreadsheet. We guessed the number of eggs the salesman may have started
with and calculated from there. The formulas needed are as follows where x is
our guess: x/2+(1/2)= y; xy= z; z/2+(1/2)=q; zq=s; s/2+(1/2)=t and; st=u. We
put the information in a table labeled with the following columns: # of eggs; #
of eggs bought by 1st customer; eggs left over from1st customer; # of eggs
bought by 2nd customer; eggs left over from 2nd customer; # of eggs bought by
3rd customer; eggs left over from 3rd customer.
Plans to Solve/Investigate the
Problem
We started with the first guess which
was the number 13. Using the above formulas, we calculated the numbers which
would go in each column. The requirements are that there can never be a fraction
of an egg and we must end up with no eggs left over.
Investigation/Exploration of the
Problem
Extensions of the Problem
As we began plugging numbers into the
formulas, we quickly saw that the number could not be even because we always
came up with a fraction of eggs and the problem reads that the man did not have
to break any eggs. As we plugged in different odd numbers, the result was that
the only number which worked with all of the given criteria from the problem
was 7. We noticed that this gave an alternating pattern of even and odd
numbers in the columns. The number 7 in the first column is odd. The number of
eggs bought by the first customer, which is the number of eggs in the second
column, is 4 which is even and so on through all 7 columns until the number in
the last column equals 0.
We used the Excel spreadsheet to do
the same problem substituting 1/3 in place of 1/2 throughout the problem, i.e.,
each customer wanted to buy one third of the salesman's eggs plus one third of
an egg. This was very difficult to do without using Excel. We tried different
guesses until we decided that we did not think it was possible. We then used
Excel the same way we made the columns on the board and our assumption was
correct. The criteria for this problem are not possible using one third in place
of one half.
Author & Contact
Pam Joseph
mailto:prj1@aol.com
Link(s) to resources, references, lesson plans, and/or other
materials
Link 1
Link 2
