Doing My Part to Destroy MSFT Productivity

I had to help a high school kid solve this problem yesterday. It’s pretty interesting I think.
I sent it around the team and people seemed to enjoy it so here you go. (In the old days, I would have saved this puzzle for an interview question, but pure puzzle questions are discouraged now.)

A census taker knocks on Mary’s door.
Census Taker: I need to know the age of your three children
Mary: The product of their ages is 36.
Census Taker: hrmmm
Mary: The sum of their ages is the same as my house number.
Census Taker: I still don’t have enough information.
Mary: The younger two are twins
Census Taker: Ok, I’ve got it now.

What are the ages of Mary’s children?

ANSWER IS NOW IN THE COMMENTS (along with a afterschool special style wrapup of what we've learned).