Question

Why does 77 minus your age plus 40 equal the year you were born?

Answer 1

Write out the entire formula, where your age is X and the year you were born is Y, and then simplify it:
Y = (77 - X) + 40
Y = 77 + 40 - X
Y = 117 - X
All you're really doing is subtracting your age from 2017 and then subtracting 1900 to get a two-digit "year."

Answer 2

You can rearrange this to say 77 plus 40 minus your age, and 77 plus 40 is 117. The year 2017 is also 117 years past the year 1900. Thus the sum in question would give you the last two digits of the year you were born. If you were born after 2000, you would have to subtract 100 from this total.