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A bridge is built across a river in 6 months by 45 men. It is washed away by the current. Required the number of workmen sufficient to build another of twice as much worth in 4 months.
The purchase price for an apple and an orange is 100 yen. When n oranges and n + 3 apples are bought the price is 520 yen. Find the number n of oranges and the price of one orange.
Historical Problems can be used to enliven any mathematics class. Here are some examples from medieval times, from a 19th century American textbook, and from a 19th century Armenian textbook, among other sources.
A survey of techniques of minimizing and maximizing over the centuries.
Paul Halmos Photograph Collection, page 3: M. Auslander, R. Baer, Banchoff, C. N. Moore, I. A. Barnett, P. Erdos, and Lida Barrett
There is a circle from within which a square is cut, the remaining portion having an area of 47.6255 square units.
I have two fields of grain. From the first field I harvest 2/3 a bushel of grain/unit area; from the second, 1/2 bushel/unit area.
This is the title page of the 1599 edition of the Rechenbuch of Simon Jacob (d. 1564), a Rechenmeister of the sixteenth century. This was a commercial arithmetic text, in which the basic laws of arithmetic were applied to many practical problems.
A brief introduction to the life of John Napier, along with an animation of calculations using Napier's bones.
Suppose the area of an equilateral triangle be 600. The sides are required.