Tuesday, December 21, 2010

Word Problem of the Week: Age of Father and Son

From Ray’s Algebra Part First by Joseph Ray, 1848.
p. 212:




If 4 be subtracted from a father's age, the remainder will be thrice the age of the son; and if 1 be taken from the son's age, half the remainder will be the square root of the father's age. Required the age of each.

Wednesday, December 15, 2010

Word Problem of the Week: Height of a May-Pole

From Pleasure With Profit: Consisting of Recreations of Divers Kinds by William Leybourne, Richard Sault, 1694, p. 35:


There was a May-Pole which consisted of three pieces of Timber, of which the first (or lowermost) was 13 foot long, the third (or uppermost piece) was as long as the lowermost piece, and half the middle piece; and the middle piece was as long as the uppermost and lowermost together: How high was this May-Pole, and how long each piece?


This is not the only problem in the book involving a maypole. I like how something so "Old-Europe" was apparently common enough in the 1690s to warrant mention in word problems. The height, by the way, turns out to be 104 feet. I've seen maypoles, but never one that tall.

Saturday, December 11, 2010

Calculus Made Easy

The prologue of a Calculus book from 1914:



This is still true today.

Wednesday, December 8, 2010

Word Problem of the Week

This is from An introduction to algebra; with notes and observations; designed for the use of schools and places of public education, by John Bonnycastle, 1806.

A labourer engaged to serve for 40 days upon these conditions, that for every day he worked he was to receive 20 d. but for every day he played, or was absent, he was to forfeit 8 d. now at the end of the time he had to receive 1 l. 11 s. 8 d. it is required to find how many days he worked, and how many he was idle.
One reason I love these old word problems is that they raise so many other questions than what "it is required to find." For example...

Was this labor arrangement something that actually happened, or is it an abstraction of a more subtle agreement? This is not the only time I have seen a problem like this one in an old book; it seems to have been a stock question in 19th century algebra books.

If this is the "First American Edition" then why does it still use British monetary units and spelling? Was the publisher just lazy?