Question

Dani is about to travel on a bus, and she knows she must tender the exact fare. She is not sure what this is, but she knows it is greater than $1 and less than $3. What is the minimum number of coins she must carry to be sure of carrying the correct fare? (Assume that the available coins are 1c, 2c, 5c, 10c, 20c, 50c, $1 and $2)

Answer 1

Combinations:

1 c = 1 c

2 c = 2 c

3 c = 1 c + 2 c

4 c = 2 c + 2 c

5 c = 5 c

6 c = 1 c + 5 c

7 c = 1 c + 2 c

8 c = 1 c + 2 c + 5 c

9 c = 2 + 2 c + 5 c

Prices 1c to 9c she can cover with the minimum number of coins:

1 x 1c , 2 x 2c and 1 x 5c


10 c = 10 c

20 c = 20 c

30 c = 10 c + 20 c

40 c = 20 c + 20 c

50 c = 50 c

60 c = 10 c +50 c

70 c = 20 + 50 c

80 c = 10 c + 20 c + 50 c

90 c = 20 c + 20 c + 50 c

Prices 10c to 90c she can cover with the minimum number of coins:

1 x 10c , 2 x 20c and 1 x 50c


For prices $1 1c to $1 99c she can cover with the minimum number of coins:

1 x $ 1 + 1 x 1c + 2 x 2c + 1 x 5c + 1 x 10c + 2 x 20c + 1 x 50c


For prices $2 to $2 99c she must have:

1 x $ 2 + 1 x 1c + 2 x 2c + 1 x 5c + 1 x 10c + 2 x 20c + 1 x 50c


For prices $1 1 c to $2 99 c the minimum number of coins she must carry:

1 x $1 + 1 x $2 + 1 x 1c + 2 x 2c + 1 x 5c + 1 x 10c + 2 x 20 c + 1 x 50 c

Total 10 coins.