Question

Fiona has 8 coins totaling fifty cents.
What combinations of coins could she have?

Answer 1

Fiona could have the following combinations of coins to total fifty cents:

5 nickels and 3 pennies: 5 x 5 cents + 3 x 1 cent = 25 cents + 3 cents = 28 cents. She would still need 22 cents, which could be made up with 2 dimes and 2 pennies.
6 nickels, 1 dime, and 1 penny: 6 x 5 cents + 1 x 10 cents + 1 x 1 cent = 30 cents + 10 cents + 1 cent = 41 cents. She would still need 9 cents, which could be made up with 1 nickel and 4 pennies.
4 nickels, 2 dimes, and 4 pennies: 4 x 5 cents + 2 x 10 cents + 4 x 1 cent = 20 cents + 20 cents + 4 cents = 44 cents. She would still need 6 cents, which could be made up with 1 nickel and 1 penny.
3 nickels, 5 dimes: 3 x 5 cents + 5 x 10 cents = 15 cents + 50 cents = 65 cents. This combination totals more than 50 cents, so it is not possible.
1 nickel, 3 dimes, and 4 pennies: 1 x 5 cents + 3 x 10 cents + 4 x 1 cent = 5 cents + 30 cents + 4 cents = 39 cents. She would still need 11 cents, which could be made up with 2 nickels and 1 penny.
So, there are three possible combinations of coins that Fiona could have to total fifty cents:

5 nickels and 3 pennies, with an additional 2 dimes and 2 pennies
6 nickels, 1 dime, and 1 penny, with an additional 1 nickel and 4 pennies
4 nickels, 2 dimes, and 4 pennies, with an additional 1 nickel and 1 penny.

Answer 2

There are different combinations of coins that could add up to fifty cents with eight coins. Here are some possible combinations:

4 quarters, 2 dimes, and 2 nickels

3 quarters, 5 dimes

3 quarters, 4 dimes, and 1 nickel

3 quarters, 3 dimes, and 5 nickels

2 quarters, 14 dimes, and 2 nickels

2 quarters, 13 dimes, and 5 nickels

2 quarters, 12 dimes, and 8 nickels

1 quarter, 20 dimes, and 2 nickels

1 quarter, 19 dimes, and 5 nickels

1 quarter, 18 dimes, and 8 nickels

17 dimes and 15 nickels

Note that there may be other combinations of coins that could also add up to fifty cents with eight coins, but these are some of the most common ones.