Intermath | Workshop Support
Write-up


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; x-y= z; z/2+(1/2)=q; z-q=s; s/2+(1/2)=t and; s-t=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
eaglepjo@aol.com

Link(s) to resources, references, lesson plans, and/or other materials
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