Coins that cannot make change for a dollar

Question

Suppose there is a pile of quarters, dimes and pennies with a total value of $1.18. How much of each coin can be present without being able to make change for $1. Explain why $1.19 is the greatest amount of money it is possible to have without being able to make change for a dollar.

Answer 1

This is a classic riddle.

3 quarters

4 dimes

0 nickels

4 pennies

 

If you have 4 quarters, you have change for 1 dollar.

If you have 5 dimes, you have change for 2 quarters.

If you have any nickels, 1 of those could combine with 2 dimes to have change for a quarter.

If you have 5 pennies, you have enough change for 1 nickel.

 

3 * .25 + 4 * .10 + 4* .01 = x

.75 + .40 + .04 = x

1.19 = x