least number of coins and greatest number of coins

Question

9. 1-1B

John goes to the store with exactly $1.00 in change. He has at least one of each coin less than a half dollar coin, but he does not have a half dollar coin.

 

a. what is the least number of coins he could have?

 

b. what is the greatest number of coins he could have?

Answer 1

a) 0.01 + .05 + 0.1 + 0.25 = 0.41

 

we know to get the least amount of coins we need as many quarters as possible that doesn't equal $1.00. So that would mean 3 quarters.

 

3(0.25) + 0.01 + 0.05 + 0.1 = 0.91 so we would need the least amount of coins to reach 0.09 cents which would be an additional 1 nickel and 4 pennies. So 3 quarters, 1 dime, 2 nickels and 5 pennies. 11 coins is the fewest.

 

b) this one is a little easier. obviously the easiest way to get the most is by pennies. Therefore using the above that 

0.01 + 0.05 + 0.1 + 0.25 = 0.41 we need 59 more pennies so 60 pennies, and 1 nickel, dime, and quarter gives 63 coins being the most.