Old Math Problems

16-year-old Helena Muffly wrote exactly 100 years ago today: 

Wednesday, September 6, 1911: Have to study in the evenings now, instead of sitting around, reading or doing nothing. I got stuck on an algebra problem this evening. Don’t know whether I’ll get it yet or not. I know how to work the problems of that kind but this is a bulky one.

Her middle-aged granddaughter’s comments 100 years later:

I suppose Grandma forgot some math over the summer.

Here are some problems in the first chapter of an algebra book that was published in 1911. Maybe the problems Grandma was struggling with were similar to these.

  1. A bicycle and suit cost $54. How much did each cost, if the bicycle cost twice as much as the suit?
  2. Two boys dug 160 clams. If one dig 3 times as many as the other, how many did each dig?
  3. The average length of a fox’s life is twice that of a rabbit’s. If the sum of these averages is 21 years, what is the average length of a rabbit’s life?
  4. The water and steam in a boiler occupied 120 cubic feet of space and the water occupied twice as much space as the steam. How many cubic feet did each occupy?
  5. Canada and Alaska together annually export furs worth 3 million dollars. If Canada exports 5 times as much as Alaska, find the value of Alaska’s export.
  6. The poultry and dairy products of this country amount to 520 million dollars a year, or 4 times the value of the potato crop. What is the value of the potato crop?

First Year Algebra (1911) by William J. Milne

For additional 1911 math problems see these previous posts:

Odd, Unusual, and Strange Math Problems

1911 Algebra Problems: The Lusitania and Molasses

1911 Algebra Problems: The Lusitania and Molasses

15-year-old Helena Muffly wrote exactly 100 years ago today: 

Thursday, March 2, 1911:  Dear me, what shall I write? Mrs. Hester was out this afternoon. I intended to work thirty-one algebra problems this evening or rather tonight but instead of that I only worked one. Perhaps I may get the remaining thirty tomorrow, but it is only perhaps.

Her middle-aged granddaughter’s comments 100 years later: 

Sometimes I have a vague idea about what I might say about a diary entry—and then I discover something interesting that sends my post in a totally different direction. Today is one of those days—

I found a high school algebra textbook published in 1911 at the library and idly flipped through the pages while pondering—Should I include some example problems from the chapter on Simple Equations  . . . or from the chapter on Quadratic Equations? And then I saw the problem on the Lusitania:

4. One ton of coal will make 8.7 tons of steam. If the Lusitania requires 1200 tons of coal a day for this purpose, how many tons of steam are required for an hour?

First Year Algebra (1911, page 157) by William J. Milne


Wait—Isn’t the Lusitania famous because it was sunk  during World War I by the Germans  in 1915? Why was the Lusitania in a textbook published in 1911?

And, as I sought answers, this post  headed in a totally different direction.

The Lusitania was a British ship that made its first trans-Atlantic trip in 1907—and it periodically held the world record as the fastest ship to make the crossing. For example, in October 1907, it held the record for an eastbound trip with a time of 4 days, 19 hours, and 53 minutes. The average speed was 24 knots/hr. (27.6 miles/hr.).

(Cruise ships today don’t cross the Atlantic as quickly as they did a hundred years ago. It now takes at least 6-7 days to make the crossing. I guess that if  someone wants to cross quickly they just fly.)

In the early 1900s there were several very fast ships that held the record at one time or another. They informally competed with one each other and the newspapers regularly reported on when the ships entered the New York harbor –or  the harbors in England on eastward trips– since there was the potential with every trans-Atlantic voyage that the world record would be broken.

A hundred years ago the general public across the US knew about the Lusitania and were following its story even before it was sunk by a German torpedo. (And, the Lusitania was apparently considered a good topic for an algebra problem since it was a timely, high-interest topic that might motivate students ).

Algebra problems provide lots of hints about what was common knowledge a hundred years ago. For example, would you ever find a problem about molasses pumps and tubing in a text today? Well, it provided the context for the word problem that followed the Lusitania problem in the 1911 textbook:

5. A grocer paid $8.50 for a molasses pump and 5 feet of tubing. He paid 12 times as much for the pump as for each foot of tubing. How much did the pump cost? the tubing?

First Year Algebra (1911, page 157) by William J. Milne

Odd, Unusual, and Strange Math Problems

15-year-old Helena wrote a hundred years ago today:

Tuesday, January 31, 1911.  If anything of real importance happened today I would write it down, but as nothing has it will not be here to read. This is the last day of the first month. What do you think of it? Vice versa.

Her middle-aged granddaughter’s comments 100 years later:

No mention of arithmetic problems in today’s diary entry. Maybe it went better today than yesterday.

I’m still fascinated by the problems in the 1911 high school arithmetic textbook that I found. The book contains some really strange problems–including some that deal with topics that probably would be considered unacceptable today.  

1. If 44 cannons, firing 30 rounds an hour for 3 hours a day consume 300 barrels of powder in 5 days, how long will 400 barrels last 66 cannons, firing 40 rounds an hour for 5 hours a day?

2. Bought by avoirdupois weight, 20 pounds of opium at 40 cents an ounce, and sold the same by Troy weight at 50 cents an ounce; did I gain or lose, and how much?

3. A wine merchant imported 1000 dekaliters of wine, at a cost of 75 cents a liter, delivered. At what price per gallon must he sell the same to clear $2000 on the shipment?

4. A certain number of men, twice as many women, and three times as many boys, earn $123.80 in 5 days; each man earned $1.20, each woman 66 1/3 cents, and each boy 53 1/3 cents per day. How many were there of each?

Kimball’s Commercial Arithmetic: Prepared for Use in Normal, Commercial and High Schools and the Higher Grades of the Common School (1911)

Remember that a hundred years ago patent medicines containing opium were legal, child labor laws were just being enacted, and it was way before woman had equal rights.

If you want to do the opium problem here are a couple of definitions:

Avoidupois weight (The usual system used in the U.S.):  16 ounces = 1 pound

Troy weight:  12 ounces = 1 pound