Ten 16th century word problems
(This post is featured in the 4th edition of the Math Teachers at Play Carnival. Check it out!)
Here are ten word problems, selected and adapted from those in the equations chapter of Robert Recorde’s Whetstone of Witte (which I am currently transcribing). This was the first English text on algebra ever published, in 1557, slightly over 450 years ago.
Some of these involve simple linear equations, while others need you to be able to solve quadratics. How many can you solve?
-
Alexander, being asked how old he was, said: “I am two years older than Ephestio.” “Yes,” said Ephestio, “and my father is as old as both of us, and four years more.” “And,” said Alexander, “all these ages added together give us 96 years.” How old is everyone?
-
I have some money owing to me. The first payment was 1/4 of the debt, and the second was 2/5 of the remainder. £27 remains unpaid. What was the original amount owed, and what were the two payments?
(The original version of this problem.) -
I have a floor paved with square bricks. The length of the floor is 1/7 longer than the breadth. The whole floor contains 3584 bricks. What are the dimensions of the pavement?
-
The captain of a large army wished to marshall them into a square formation, as large as possible. In his first attempt, he had 284 soldiers too many. Increasing the size of the square by one, he found he was 25 men short. How many soldiers did he have?
-
A king’s advisor was given a bribe, and made to swear that he would tell the king’s enemy how many dukes, earls, and other soldiers there were in the army. The advisor wanted to keep the bribe, but did not want to betray his king, so gave his answer in the form of the following riddle:
Look how many dukes there are, and for each of them there are twice as many earls. Under every earl there are four times as many soldiers as there are dukes. And when the muster of the soldiers was taken, the 200th part of them was 9 times as many as the number of dukes.
How many of each type were there?
-
A poor man with four children died. He had saved 72 crowns, and in his will wanted this split with the following conditions:
- The second and third child should together have 7 times as much as the first.
- The portions of the third and fourth child together should be 5 times as much as the second’s part.
- The first and the fourth together should have twice as much as the third.
How much did each child receive?
-
A gentleman, wishing to test the cunning of a bragging mathematician, said: “I have, in my hands, 8 crowns. If I take the amount in each hand, and add that together with the squares and cubes of both numbers, it will make in total 194. Tell me what I have in each hand, and I will give it to you.”
-
A man has been asked to go on a strange journey. The first day, he must go 1 1/2 miles. Every day after the first he must go 1/6th of a mile further than the day before. The length of his journey is 2955 miles. How many days will his journey take?
-
There is a number, which I have forgotten, divided into 2 parts, one of which is 4, and the other I have also forgotten. I do remember this, though: if the part I forgot is multiplied by itself, and then also multiplied with the 4, those two numbers added together will make 117. What, then, was the whole number, and what was the part I forgot?
-
Two men are talking together about money. “The number of coins in my pocket,” says the first man, “may be divided into two numbers which make 24 when multiplied together. And the cubes of these numbers, added together, make 280.” “I may say the same about my coins,” says the other man, “except that the cubes of the two parts will make 539.” How many coins did each of them have?
(The picture is Mary Tudor, Queen of England at the time the Whetstone of Witte was published.)
