Friday, August 31, 2012

Try these word problems from 1900's "School Arithmetic Advanced Book"

This is the cover of the 1900 math textbook "School Arithmetic Advanced Book," which was written by John M. Colaw and J.K. Ellwood.1

It was part of the Johnson Series, which also included a 271-page, 35-cent Primary Book.

The book's ambitious contents include:
  • Notation and Numeration of Integers
  • Tests of Divisibility
  • Aliquot Parts
  • Measures of Value, Capacity, Weight, Extension, Volume and Time
  • Longitude and Time
  • The Metric System
  • Profit and Loss
  • Simple Interest, Annual Interest and Compound Interest

There is also a section on Practical Measurements, including discussions of using mathematics for painting, plastering, measuring lumber, brick work, stone work, carpeting and papering. Handy stuff!

Now, as we're getting back into the swing of the school year, try your hand at some of the word problems featured in the textbook.2 The answers are down below, under the footnotes.

A. A farmer bought two cows, giving $29.50 for one and $36.75 for the other. He gave in payment a wagon worth $42.25, and the rest in cash. How much money did he give?

B. If 20 bushels of wheat produce 6¼ barrels of flour, how many bushels will produce 100 barrels?

C. If 9 compositors can set up a 6-page paper in 8 hours, in how many hours can they set up a 20-page paper?

D. Sixty men can grade a street in 40 days. After 24 days, one third of the men are discharged. In how many days can the others finish the work?

E. A farm is worth 10% less than a store, and the store 20% more than a lot. The owner of the lot exchanges it for 80% of the farm, thereby losing $850. What is the farm worth?

F. A man has a library of 1,600 volumes. 14% are biography, 62% are history, and 83½% of the remainder are fiction. How many volumes of fiction in his library?

1. Here's a neat inscription from 1902 on one of the book's first pages:

2. I realize that barraging readers with a series of math word problems is probably not the best way to encourage them to return to Papergreat. But I'm trying to mix it up. It can't be all about fluffy chickens and root-beer advertisements here. We need some variety!

A. $24
B. 320 bushels
C. 26⅔ hours
D. 24 days
E. $6,750
F. 320 volumes


  1. Interesting. Thanks :)

  2. I like these. Perhaps I'm wrong but it seems like the answer to question d) would be 48 days and not 24? If 1/3 of the workers were released it would take 3 times as many days to do the same job. If it would have taken the full crew of 60 men an additional 16 days to complete the work then it stands to reason that it would take 20 men 48 days to complete the same task.

  3. Oops I am wrong. 1/3 of the workers released. That means 2/3 remain. That would be a factor of 1.5 times the number of days to do the job. 16 days x 1.5 = 24 days.