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.

Word Problem of the Week: Wainscoting a Gentleman's House

From A Compendium of Algebra by John Ward, 1724.

p. 51:

Three Joiners undertook to wainscot a Gentleman's House in 150 days. One of then (being esteem'd the best) was to have 5 s. a day for every day he work'd; another was to have 4 s. 6 d. a day, and the third was to have but 4 s. for every day we wrought.
When the Work was finish'd, every one of them had just the same Sum of Money to receive; Quere, how many Days each of them work's? &c.

So, they all made the same amount, which makes me wonder: Is the highest-paid worker the best because he's the most efficient, or is he doing a bit of slacking off?

Word Problem of the Week: Arraying the Troops

From The Elements of that Mathematical Art Commonly Called Algebra, Expounded in Two Books by John Kersey, 1741.

p. 70:

A General of an Army having set his Soldiers in a Square Battel, there happened to be 500 (or b) Soldiers to spare; but to increase the Square so as that its side might consist of 1 (or c) Soldier more than the Side of the former Square, there would be 29 (or d) Soldiers wanting. The Question is, to find how many Soldiers the General had in his Army.

Word Problem of the Week: A Brandy Smuggler

From Ray’s Algebra, Part Second by Joseph Ray, 1852. p. 91:

A smuggler had a quantity of brandy, which he expected would sell for 198 shillings; after he had sold 10 gallons, a revenue officer seized one third of the remainder, in consequence of which he sells the whole for only 162 shillings. Required the number of gallons he had, and the price per gallon.

My favorite part of this problem is the story we aren't getting. Why did the revenuer only confiscate a third of the brandy? My two best guesses are that the "seized" brandy was actually given to the revenuer as a bribe to ignore the rest, or that only one stash of several got raided.

This is apparently the sort of thing that seemed relevant to algebra students living at a time when the Whiskey Rebellion is in living memory.