If you go into the formula you can see why it works:

If the number you chose is x, you double it, so you get 2 x
Then you add 5 and get 2 x + 5
Then you multiply it all by 50 and get (2x+5) * 50
That is 100 x +250
Then you either add 1755 or 1756
Means you have 100 x +250 + 1755
or
100x + 250 +1756
which is either 100x +2005 (if your birthday was not yet this year) or 100x+2006 (if your birthday was already this year).
You now can see that if you deduct your birth year from the 2005 or 2006 you obviously get your age.

And multiplying your chosen number x by 100 gets it at the first digit of the resulting 3 digit number.

Next year it will work again, but you'll have to add 1756 or 1757