Age Doesn't Matter!

My friend Norma asked me a question last night via Facebook. For practical purposes, I am rephrasing her question as:

Why is the sum of the person's two-digit birth year and that person's age plus one always equal to 111?

Norma, who is now 34, was born in '76. She observed that 76 + 34 + 1 = 111.

I thought of Matty. He was born in '83. Last year, he turned 27.  Observe that 85 + 25 + 1 = 111.

My student Alisha, who was born in '96, celebrated her 14th birthday last year. Well, 96 + 14 + 1 = 111.

"So why does this work?," Norma insisted.

Readers, what do you think?


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SOLUTION:
When you say your birth year is 76, you actually mean 1976, which is 1900 + 76.

So if your birth year is X, then it is actually (1900 + X).

If you were born in the year (1900 + X), then in the year 2010, your age was [2010 - (1900 + X)] years old.

So your birth year plus your age plus one
= X + [2010 - (1900 + X)] + 1
= X + 2010 - 1900 - X + 1
= 111.

It doesn't matter how old the person is, the result will always be 111.


Norma's question reminded me of a similar problem. Last December, in a statewide conference I attended in Dallas, the following question (that I also rephrased) was raised for us to play with:

Add your age by the end of this year to the year you were born. What do you get?

Now your turn. Prove why it works.