While traveling through a remote part of Utah, Donny and Marie came upon the strange little town of Stubs. Though the people of Stubs are familiar with traditional U.S. currency, they only use it when transacting with outsiders. Most often, they use a currency that is best described in the following way:

• One copper coin is worth one U.S. penny
• One silver coin is worth five copper coins
• One gold coin is worth five silver coins
• One green bill is worth five gold coins
• One red bill is worth five green bills
• One blue bill is worth five red bills
• Bills of greater value exist, but are rarely used

At first, Donny and Marie were confused by this new currency, but the mayor of the town explained that Stubs officially uses a base-five number system. The reason for this became clear as the mayor led them to a statue of the town's founding father. The statue paid tribute to a one-armed man whose name was William ``Stubs'' Reynolds. The plaque beneath the statue claimed that the town of Stubs was founded in 24311₅.

1. Find the equivalent value in U.S. dollars to each of the currencies listed above.
2. The mayor treated Donny and Marie to lunch at a local diner. The total bill came to 43100₅.
   1. How should the mayor pay the bill if she wishes to use the fewest bills and coins?
   2. How would you write a price that could be paid with one blue bill and one gold coin?
3. While glancing through a book on local tourist attractions, Marie noticed that the pages were numbered in the following way:

   15,25,35,45,105,115, ...

   She counted that there were 26 pages in all. Write down the entire sequence of page numbers as they appeared in the book.
4. Marie decided to buy the book on tourist attractions. The price was 2144₅.
   1. How much should Marie pay in U.S. dollars?
   2. If Marie paid with a U.S. five dollar bill, what change, in Stubs currency, should she expect?
5. What is the traditional way to write the year in which Stubs was founded? How would the current year be written in Stubs?
6. Why do you think the people in Stubs use a base-five number system?
7. In order to better understand different numeration systems, research ancient number systems. Write several paragraphs describing what you find.