Robert Belanger (21 Jan 2011)
"Katy Re 111"

Katy,
 
You said:
 
"I saw this on face book ... Considering all the 1's I knew some one on here would want to see this . I was born in 1964 this year I will be 47+64 = 111. Add yours up and see how it comes out the last two of the year you were born and how old you will be this year.
                 Well God Bless all of His Children in Jesus Name I ask.
                                                                  Katy"
Many of us studied geometry and algebra in our youth and wondered where these subjects could ever be useful in everyday life. Well, this is an example of their practical use.
 
----------------------------
 
TP: To prove that any year of birth after 1900 will sum to 111 when added to the person's age in 2011:
 
Using the following diagram where 1900 and 2011 represent the years 1900 AD and 2011 AD:
 
1900              YOB                                  2011
    [<-----x------->][<------------ y -------------->]
 
and YOB is equal to the last two digits of the Year of Birth, ( By the way, for those who can think in visual form, from the diagram, it is easily seen by inspection that y is ALWAYS equal to  111-x).
 
This apparent truth can also be proved by geometry and algebra as follows:
 
Let x be the number of years after 1900 when the person was born, i.e., the right-most two digits of the person's YOB,
 
Let y be the age of the person in 2011,
 
Adding the two consecutive line segments representing the years x and y in the diagram, we have,
 
x + y = (2011 - 1900)   [Eq. 1]
 
or,
 
x + y = 111             [Eq. 2]
 
QED (quod erat demonstrandum)
 
Here is a numerical example:
 
Given that a person born in 1950 and will naturally be 61 years of age this year of 2011. 
 
From the diagram and the derived equation, [Eq 2]
 
x = 50
 
y = 61
 
and by substitution into equation [Eq 2] of the numerical values for x and y:
 
x + y = 111
 
50 + 61 = 111.
 
As is apparent, any Year of Birth after 1900 and age in 2011 sum to 111.