Word Problem of the Week: From the Notebook of Benjamin Banneker

This morning I had the pleasure of attending a talk by John Mahoney concerning his experience teaching at Benjamin Banneker Academic High School in the District of Columbia. Part of the talk concerned Banneker himself, who is a fascinating personality about whom I'm going to have to write more later.

Banneker kept a notebook in which he recorded interesting problems. This one is interesting because there is an elegant solution that is unintuitive to someone educated in the modern way. At least to me, it was unintuitive. Problems such as this seem to have been popular in the 18th century, though.

Question by Elliot Geographer General
Divide 60 into four Such parts, that the first being increased by 4, the Second decreased by 4, the third multiplyed by 4, the fourth part divided by 4, that the Sum, the difference, the product, and the Quotient shall be one and the Same number.

You start by making a guess as to the number mentioned at the end, then adjust things based on the error you get.