Imagine a country that has only 2 denominations of currency: $7 bills as well as $11 bills. How would the economy work in this country?
There are 2 different ways to make $120. For example, you can employ three $7 bills and nine $11 bills or you can employ fourteen $7 bills and two $11 bills
A) Determine the largest amount of money which can be made in exactly one way? Discuss why there is only one way to make a stack worth this amount.
B) Determine the smallest amount which can be made in two different ways? What about three different ways? What about four ways? What about five? Is there a pattern?
C) Using only $7 and/or $11 bills, there are thirteen different manners to make a stack of money worth exactly $1000. Find out all of them. Discuss the system you used to find them.