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Play a Game of Young Maid

A maid being asked her age, replied
If it by three be multiplied,
Two sevenths of that product ta'en,
And multiplied by three again.
Two ninths of this will then be seen
Not more nor less than just sixteen
From these few hints my age explore
Or never dare to ask me more.


Solution:

Source: Student's hand-written mid-19th century arithmetic copy book (sold on on ebay, 8/13/05)