Mike Turnbull Algebra Learning Resources - A Hen and a Half

Mike Turnbull (previously CQSRG 2002 to 2021) has been researching the earthquake seismicity of Eastern Central Queensland since 2002.
Mike Turnbull is a self funded, independent, non-commercial researcher.

Using Algebra to solve a Silly Problem

By Mike Turnbull

When teaching children algebra it sometimes helps to use algebraic problems disguised as silly questions. This is one such silly proplem - I dont know when or where I first heard it, but it has been in my head since I was a child. The question is posed as a riddle, as follows.

If a hen and a half lays an egg and a half in a day and a half, how many eggs will one hen lay in a week?

Let x be the number of eggs one hen will lay per day.

We need to determine a value for x such that:

   
   Number of eggs
   per day       *     1 1/2 hens    *   1 1/2 days   =   1 1/2 eggs
   for one hen
   
       x         *         1 1/2     *     1 1/2      =   1.1/2  [where 1 1/2 * 1 1/2 = 2 1/4]
       
       x         *         2 1/4     =     1 1/2
       
       Now divide both sides of the equation by 2 1/4
       
       x         =         1 1/2     /     2 1/4         [where 1 1/2 divided by 2 1/4 = 2/3]
       
       x         =           2/3

Now we simply multiply x by the number of days in a week.

   
       x  *  7  =  2/3  * 7  =  14/3  =  4 2/3