As my younger brother shouted out four consecutive inegers, I divided each by my age...?

Question

As my younger brother shouted out four consecutive inegers, I divided each by my age (an integer), then added all four remainders to get 40. As he shouted out four other consecutive integers, I divided each by his age (a different integer), added all four remainders, and again got 40. What is the sum of our ages? Any help would be appreciated. Seems sorta easy but I can't figure out a working formula.

Answer 1

Unless you're in a base other than 10 (which is the base we typically use), I don't see how you can add four remainders to get 40.

In our number system, the largest remainder you can get when you divide is 9, so even if you get a remainder of 9 for all four divisions, that's only 36.

Answer 2

I would use x and put x+1, x+2, x+3...or something like that for the consecutive numbers. You have to set up an equation. Or just use guess and check! Sorry I couldn't help out any more :(