الأربعاء، 9 يناير 2013

A math puzzle for Marco Polo

I found this passage in Marco Polo and the Discovery of the World, by John Larner:
"In Venice, merchants' sons... normally had only the most superficial contact with the Latin learning of the grammar schools.  Their education was almost wholly devoted to their future vocation

A prime exhibit here is the fourteenth-century miscellany known as the Zibaldone da Canal.  This is a mercahnt's commonplace book, which was elaborated from a student's workbook of mathemtical problems... the Zibaldone (meaning 'Miscellany' or 'Ragbag') places the strongest emphasis on practical arithmetic... As for example (here I cite the admirable translation of J.E. Dotson):
Make me this calculation: 2 merchants have their wool on a ship.  One of them put 13 sacks and the other of them put 17 sacks [on board].  And when they had arrived in Venice the captain demanded his freight charges from the merchants and they said to him, 'Take one of our sacks from each of us and sell it and pay our freight costs and return the remainder.'  And the captain took 2 of those sacks and sold them and gave 10s. from the proceeds to him who had 13 sacks after the freight had been paid.  And he returned 3s. to the man who had 17 sacks and his freight was entirely paid.  And the merchants said to the captain, 'We want to know how much you sold the sacks for, and how you calculated what you took from it for freight charges.' [Follows the explanation of how the sum is done].
I've put my answer below the fold.
I come up with 1.75s for the cost of freight per sack, and 32.75s as the amount for which each sack was sold.

Right?  (The answer is not given in the book).

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