MAT 336 Stony Brook University
Word Problems from the Treviso Arithmetic - 1478
[comments in square brackets]
(f. 35r) 1 and 1/2 pounds of saffron are worth 2 and 1/3 ducats [maybe $230; saffron is currently on sale on eBay for $205/lb.] how much would 1 and 1/4 ounces be worth. [One pound is 12 ounces, one ducat is 24 grossi, one grosso is 32 piccioli. Express your answer in grossi (g.) and piccioli (p.).]
Answer: If 1 and 1/2 pounds of saffron are worth 2 and 1/3 ducats then 1 and 1/4 ounces are worth g.3 p.28 and 4/9.
(f. 44r) I have 9 and 2/3 yards (braccia) of fabric 2 and 3/4 yds wide which I want to make into a robe. I want to line it with fabric 1 and 1/8 yds wide. I ask how much I will need.
Answer: I will need 23 and 17/27 yds. [The text has the wrong answer, due to a trivial arithmetic error, making 232x11=1552 instead of 2552.]
(f. 46v) Three merchants have invested their money as a company. Let's give them names to make this easier to understand. The first is Piero. The other is Polo. The third is Zuanne. Piero put in as his capital 112 ducats [maybe $11200]. Polo put in as his capital 200 ducats. Zuanne put in as his capital 142 ducats. And at the end of a certain period of time they have realized a profit of 563 ducats. I ask how much each man gets so that no one will be cheated.
Answer: You answer that Piero gets as profit ducats 138 g.21 p.11 and 190/454. Polo gets as profit ducats 248 g.0 p.13 242/454. Zuanne gets as profit ducats 176 g.2 p.7 and 22/454. No one will be cheated. The sum of the profit is duc.563 g.0 p.0/454, which shows that this argument was done correctly.
(f. 46v) Two merchants, that is Sebastiano and Jacomo have invested their money to make profit as a company. Sebastiano contributed duc.350 on January 1, 1472. Jacomo contributed duc.500 g.14 on July 1, 1472. On January 1, 1474 they have realized a profit of ducats 622. I ask how much each one gets.
Answer: You answer that Sebastiano gets as profit duc.300 g.2 p.8 and 327456/417852. Jacomo gets as profit duc.321 g.21 p.23 and 90396/417852. The sum of the profit is duc.622 g.0 p.0/417852 so this sharing was done justly and well.
(f. 53v) A merchant has 40 marks of silver alloy [one mark is 8 ounces] with 6 and 1/2 ounces per of pure silver per mark. And he has 56 marks of another alloy, with 5 ounces of pure silver per mark. And he wants to make all of this into coinage which will contain 4 and 1/2 ounces of pure silver per mark. I ask how much coinage he will produce and how much copper he will have to add.
[Answer: The amount of coinage he can produce is 120 marks. The amount of copper he must add is 24 marks.]
October 15 2006