Homework due Friday, September 2, 2011

Problem 1: You have 2 dollars. You want to spend it all on candy. Mints cost a nickel, and Milky Ways cost 21 cents. How many of each should you buy to use up your 2 dollars? Is there any solution? Is there more than one solution? How can you decide?

Try to solve this using the strategy discussed in class Fri Sep 2: first solve gcd(5,21) = x5 + y21. In other words, since gcd(5,21)=1, first solve 1 = x5+y21. Then multiply through by 200 to get a solution to 200=m5+n21. Now add multiples of 21*5 - 5*21 to get a solution where m and n are both non-negative.