In 1912 Arthur Finnegan purchased an old house. While he was replacing some loose floorboards he was very excited to find an old sack of money buried under the floor. His excitement soon dissipated, however, when he realised the sack contained only coins. There were 100 coins in all (US currency), with a total worth of $5. The sack did not contain any nickels. What coins were in the sack, and how many of each were there?

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There were 60 pennies, 39 dimes, and one half dollar.

Another solution: 90 pennies + 1 dime + 2 quarters + 7 half-dollars

Actually, a family of solutions:

1 half-dollar + 39 dimes + 60 pennies

1 half-dollar + 3 quarters + 31 dimes + 65 pennies

1 half-dollar + 6 quarters + 23 dimes + 70 pennies

1 half-dollar + 9 quarters + 15 dimes + 75 pennies

1 half-dollar + 12 quarters + 7 dimes + 80 pennies

4 half-dollars + 1 quarter + 20 dimes + 75 pennies

4 half-dollars + 4 quarters + 12 dimes + 80 pennies

4 half-dollars + 7 quarters + 4 dimes + 85 pennies

7 half-dollars + 2 quarters + 1 dime + 90 pennies

Any others?

Still more…

– 90 pennies, 6 dimes, one half dollar, 3 dollars

– 90 pennies, 1 dime, 4 quarters, 4 half dollars, 1 dollar