1 You find yourself in a strange country where there are onl

1. You find yourself in a strange country where there are only two kinds of coins: a 13 dollar coin and a 7 dollar coin.

(a) If you have to pay a bill of 175 dollars, describe all possible combinations of coins you can use to pay this exact amount with no change needed. Justify your answer.

(b). You have to pay a bill of 50 dollars. Show that you cannot pay this exact amount in coins, but find at least two ways to pay this bill if the cashier gives you change back. Find, with justification, the way to do this for which the amount of change the cashier has to give you back is the smallest possible.

Solution

given

13 doller coin

7 doller coin

i. no change given two way

they are i.all 25 coins of 7 dollers

ii. 12 coins of 7 and 13 coins of 7

ii. with change

i . take 7 coins 6 and 1 coin og 13

ii take 13 coins of 3 and 7 coins of 2