1. Exploration. a. The King trades his coins at the bank, according to their official value, with the object of having as few coins as possible in the tiny pocket of his slinky new pants. He starts with 1000 florins. What does he end up with? b. Prince Enbel has one ducat. He buys a toastereo (a popular appliance which, unfortunately, does not make coffee), costing 50 ecus. If he is given the fewest coins possible, how much change does he get? c. Princess Lisa has one ecu. She wins the first prize in a contest in Names Magazine. The prize is one ducat, one ecu, and one florin. She now has four coins, but they won't fit into her pocket. What does she have after trading them in to get as few coins as possible? (The second prize would have been a T-shirt with the Names logo and no pockets at all.) d. Sol Grundy has no money. He gets a job at the toastereo store, earning one florin per day, seven days a week. Since his pockets are fashionably small, he trades his money as often as possible in order to have as few coins as possible. If he starts his new job on Monday, how much does he have each day of the week? And the next week? (Assume he doesn't spend any money.)
1. Exploration. a. The King trades his coins at the bank, according to their official value, with the object of having as few coins as possible in the tiny pocket of his slinky new pants. He starts with 1000 florins. What does he end up with? b. Prince Enbel has one ducat. He buys a toastereo (a popular appliance which, unfortunately, does not make coffee), costing 50 ecus. If he is given the fewest coins possible, how much change does he get? c. Princess Lisa has one ecu. She wins the first prize in a contest in Names Magazine. The prize is one ducat, one ecu, and one florin. She now has four coins, but they won't fit into her pocket. What does she have after trading them in to get as few coins as possible? (The second prize would have been a T-shirt with the Names logo and no pockets at all.) d. Sol Grundy has no money. He gets a job at the toastereo store, earning one florin per day, seven days a week. Since his pockets are fashionably small, he trades his money as often as possible in order to have as few coins as possible. If he starts his new job on Monday, how much does he have each day of the week? And the next week? (Assume he doesn't spend any money.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:On the treeless planet of Glosia, the currency consists of florins, ecus, and ducats. **One florin is worth two ecus, and one ecu is worth two ducats.** Since there is no paper, there is no paper money, and the people of Glosia have to carry coins everywhere. King Evariste VII, being immensely rich, must wear bloomers with enormous reinforced pockets to hold his money.
One day, the King realizes that there is a new trend in Glosian fashion: elegant men and women wear only small pockets. Evariste VII, not one to be left behind by the great movements of style, decides to institute a drastic economic reform, by enacting a strange law: **One ducat is worth two florins!** (The old rules are not changed.) When you realize trades can be made in either direction, you can see how the King’s brilliant legislation will abolish poverty forever!
The people of Glosia are ecstatic. With the new system, one may have a fortune in one’s pockets, and yet never carry more than three coins! One can be rich and fashionable at the same time. For example, if you own eight ecus, you can go to the bank, and trade them in for four florins. These can be traded again, for two ducats, which equal one ecu, which will certainly fit in your pocket.
Transcribed Image Text:**Exploration**
a. The King exchanges his coins at the bank to minimize the number of coins in the pocket of his new pants. He begins with 1000 florins. The task is to determine how many coins he ends up with.
b. Prince Enbel possesses one ducat. He purchases a toastereo, costing 50 ecus. The challenge is to calculate the change he receives in the fewest coins possible.
c. Princess Lisa has one ecu. Upon winning a contest in *Names Magazine*, she receives one ducat, one ecu, and one florin, resulting in a total of four coins. However, they do not fit in her pocket. The goal is to determine the number of coins she will have after trading them in for as few coins as possible.
d. Sol Grundy starts with no money and earns one florin per day, working seven days a week at a toastereo store. He exchanges his earnings frequently to minimize the number of coins due to his small pockets. Analyze how much money Sol has at the end of each day of the first and second week, assuming no expenditure.
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