When First the Marriage Knot was Ty'd

This little puzzle comes from a book honoring the great puzzle master Martin Gardner.  In the chapter titled Some Diophantine Recreations, David Singmaster presents the following poem which appeared in The American Tutor’s Assistant, in 1791.


When first the marriage knot was ty’d
Between my wife and me,
My age was to that of my bride
As three times three to three
But now when ten and half ten years,
We man and wife have been,
Her age to mine exactly bears,
As eight is to sixteen;
Now tell, I pray, from what I’ve said,

What were our ages when we wed?