Consecutive integers?

Ive been working out of a high school math book that my dad grabbed for me(since he is a custodian in a high school) and im up to the chapter involving equations with consecutive integers.
It dosen't seem that bad but i am not sure if the result of this equation is correct. it should be but i just want to double check. :)

The ages in years of three brothers are consecutive. The sum of their ages is 39 decreased by the age of the youngest. What are their ages?

I come up with the following....

a + (a + 1) + (a + 2) = 39 - a

3a + 3 = 39 - a

3a + a + 3 = 39 - a + a

4a + 3 = 39

4a + 3 - 3 = 39 - 3

4a/4 = 36/4

a = 9

So their ages must be 9,10,11

Does this look correct?

Yes, it appears correct. :)

Thanks for the double check. :)

A handy trick when using consecutive integers is to have "a" as one of the middle terms.
i.e. let there ages be a-1, a, a+1
This way, if you have to use their product, it is
=a*[(a+1)*(a-1)] -diff. of squares
=a(a^2-1)
=a^3 - a

This is much easier to work with than:
=a*(a+1)*(a+2)
= a*(a^2+3a+2)
= a^3+3a^2+2a