What is the mathematical explanation for this trick?

Question

I found the following method to find one's age. It is working exactly for my case. I like to understand and solve this puzzle. If this is wrong forum, my sincere apologies. Please guide me solve this.

1. Take last digit of your mobile number
2. Multiply it by 2
3. Add 5 with the above answer
4. Multiply the answer with 50
5. Add 1764 with the answer
6. Subtract the your birth year from the result in part 5 (example 1985, 1973, etc.)

Now you will get 3 digit number. The first one is last digit of your mobile number, last two digits are your age.

Answer 1

1. Let $n$ be the last digit of your mobile number.
2. $2n$
3. $2n+5$
4. $50(2n+5)=100n+250$
5. $100n+250+1764=100n+2014$ (fixed by Daniel R)
6. Let $y$ be your year of birth. Then we have $100n+(2014-y)$.

Since $2014-y$ is your age (assumed to be $<100$), the hundreds digit is $n$ and the last two digits are your age.

Answer 2

$50(2x + 1) + 1964 - y = 100x + (2014 - y).$

If you were born before August 1st in year y, then (2014 - y) is your age. If you are under 100, then it's a 2-digit number. So the right-hand side of the equation is just a three digit number whose first digit is $x$ (doesn't matter what one-digit number $x$ we started with) and whose last two digits are your age.

edit: fixed lhs as per comments

Answer 3

That's elementary. If $d$ is the last digit and $y$ your birth year, you are computing

$$(2d+1)50+1964-y=100d+2014-y.$$

The first term is the digit shifted two positions to the left (times $100$); the other two terms compute your age.

You'll have to increment the constant $1964$ every year, and the trick won't work for centenarians.