Question

Discrete Math Problem Joe and Harry go to a restaurant. Joe forgets his wallet at home, so Harry pays for both meals. Joe is going to pay Harry back in cash the next day, but he mistakenly grabs his French wallet containing only Euros. Luckily, Harry is planning a trip to Europe and will be happy to accept the Euros. Thus, they arrange to do an exchange. At the time of this transaction, the exchange rate is 5 $3USD (5:3) and Joe has a large supply of 5 bills while Harry has an equally large supply of US $5 bills. QUESTIONS: A. Prove that Joe can pay Harry exactly $4USD in value, through only the exchange of S bills and $5 bills. Suppose they went to a fancier restaurant which costs more. Generalize your answer to (A) to show that for all positive integers x representing money owed by Joe to Harry, an exact payment can be made. Give an expression for how many bills must change hands and briefly explain it. B. C. Suppose that suddenly the world currency markets are rocked and the S bill is now worth b USDs, for some integer b. Generalize your answers to (A) and (B) to show that for all positive integers x representing money owed by Joe to Harry, an exact payment can be made for a currency exchange of 5 bills and $5 bills. D. Lastly, suppose Harry runs out of $5 USD bills and Joe runs out of S bills. Fortunately, Harry discovers that he has a big supply of identical Mexican Pesos, each of which is worth p USD. Likewise, Joe discovers that he has an equally large supply of Japanese Yen notes, each of which is worth y USD. Assuming p and y are integers, give an expression for how many bills must change hands to make an exact payment and briefly explain it.

Answer 1