George has 2 quarters, 2 dimes and 2 nickels. Using at least one of the 6 coins, how many different amounts of money can he make?

Q - D - N --- cents

1 1 1 -- 40
1 1 2 -- 45
1 2 1 -- 50
1 2 2 -- 55
2 1 1 -- 65
2 1 2 -- 70
2 2 1 -- 75
2 2 2 -- 80

looks like 8 different sums

(I listed them all, just in case a different combination would yield the same sum)

misread the question, there are more

Q D N
0 0 1 -- 5
0 0 2 -- 10
0 1 0 -- 10 ***
0 1 1 -- 15
0 1 2 -- 20
0 2 0 -- 20 ***
0 2 1 -- 25
0 2 2 -- 30
1 0 0 -- 25 ***
1 0 1 -- 30
1 0 2 -- 35
1 1 0 -- 35 ***
1 1 1 -- ***
1 1 2 -- ***
1 2 1 -- ***
1 2 2 -- ***
2 0 0 -- ***
realize that we have the rest already

I suddenly realized that the smallest coinage we can have is
001 or 5 cents, and the largest
222 or 80 cents, and we can obtain every multiple of 5 in between

for a total of 16 different sums

To find the different amounts of money that George can make using the given coins, we need to consider all possible combinations of the coins.

George has 2 quarters, 2 dimes, and 2 nickels. Let's consider each coin separately:

1. Quarters: George can use 0, 1, or 2 quarters. These three options correspond to the amounts of $0.00, $0.25, and $0.50, respectively.

2. Dimes: George can use 0, 1, or 2 dimes. These three options correspond to the amounts of $0.00, $0.10, and $0.20, respectively.

3. Nickels: George can use 0, 1, or 2 nickels. These three options correspond to the amounts of $0.00, $0.05, and $0.10, respectively.

Now, let's combine the three options for each coin. We have:

- Using 0 quarters, 0 dimes, and 0 nickels gives an amount of $0.00.
- Using 1 quarter, 0 dimes, and 0 nickels gives an amount of $0.25.
- Using 2 quarters, 0 dimes, and 0 nickels gives an amount of $0.50.
- Using 0 quarters, 1 dime, and 0 nickels gives an amount of $0.10.
- Using 1 quarter, 1 dime, and 0 nickels gives an amount of $0.35.
- Using 2 quarters, 1 dime, and 0 nickels gives an amount of $0.60.
- Using 0 quarters, 2 dimes, and 0 nickels gives an amount of $0.20.
- Using 1 quarter, 2 dimes, and 0 nickels gives an amount of $0.45.
- Using 2 quarters, 2 dimes, and 0 nickels gives an amount of $0.70.
- Using 0 quarters, 0 dimes, and 1 nickel gives an amount of $0.05.
- Using 1 quarter, 0 dimes, and 1 nickel gives an amount of $0.30.
- Using 2 quarters, 0 dimes, and 1 nickel gives an amount of $0.55.
- Using 0 quarters, 1 dime, and 1 nickel gives an amount of $0.15.
- Using 1 quarter, 1 dime, and 1 nickel gives an amount of $0.40.
- Using 2 quarters, 1 dime, and 1 nickel gives an amount of $0.65.
- Using 0 quarters, 2 dimes, and 1 nickel gives an amount of $0.25.
- Using 1 quarter, 2 dimes, and 1 nickel gives an amount of $0.50.
- Using 2 quarters, 2 dimes, and 1 nickel gives an amount of $0.75.
- Using 0 quarters, 0 dimes, and 2 nickels gives an amount of $0.10.
- Using 1 quarter, 0 dimes, and 2 nickels gives an amount of $0.35.
- Using 2 quarters, 0 dimes, and 2 nickels gives an amount of $0.60.
- Using 0 quarters, 1 dime, and 2 nickels gives an amount of $0.20.
- Using 1 quarter, 1 dime, and 2 nickels gives an amount of $0.45.
- Using 2 quarters, 1 dime, and 2 nickels gives an amount of $0.70.
- Using 0 quarters, 2 dimes, and 2 nickels gives an amount of $0.30.
- Using 1 quarter, 2 dimes, and 2 nickels gives an amount of $0.55.
- Using 2 quarters, 2 dimes, and 2 nickels gives an amount of $0.80.

Therefore, George can make a total of 26 different amounts of money using at least one of the 6 coins.