Friday, January 10, 2014

A challenge for the math historians in the audience

I came across this while working on a Pólya project. The following is a standard collection of word problems but the first five share a notable attribute while the last has a different but similar one.

Any guesses?
A mule and an ass were carrying burdens amounting to some hundred weight. The ass complained of his, and said to the mule: “I need only one hundred weight of your load, to make mine twice as heavy as yours.” The mule answered: “Yes, but if you gave me a hundred weight of yours, I should be loaded three times as much as you would be.”
How many hundred weight did each carry ?

A father who has three sons leaves them 1600 crowns. The will precises, that the eldest shall have 200 crowns more than the second, and the second shall have 100 crowns more than the youngest. Required the share of each.

A father leaves four sons, who share his property in the following manner:
The first takes the half of the fortune, minus 3000 livres.
The second takes the third, minus 1000 livres.
The third takes exactly the fourth of the property.
The fourth takes 600 livres and the fifth part of the property.
What was the whole fortune, and how much did each son receive?

A father leaves at his death several children, who share his property in the following manner:
The first receives a hundred crowns and the tenth part of what remains.
The second receives two hundred crowns and the tenth part of what remains.
The third takes three hundred crowns and the tenth part of what remains.
The fourth takes four hundred crowns and the tenth part of what remains, and so on.
Now it is found at the end that the property has been divided among all the children. Required, how much it was, how many children. there were, and how much each received.

Three persons play together; in the first game, the first loses to each of the other two as much money as each of them has. In the next, the second person loses to each of the other two as much money as they have already. Lastly, in the third game, the first and second person gain each from the third as much money as they had before. They then. leave oil and find that they have all an equal sum, namely, 24 louis each. Required, with how much money each sat down to play.

Three Workmen can do a Piece of Work in certain Times, viz. A once in 3 Weeks, B thrice in 8 Weeks, and C five Times in 12 Weeks. It is desired to know in what Time they can finish it jointly.