How many ways can you have $1.05, with only using dimes, nickels, and quarters?

How many ways can you make $1.05 with only dimes, nickels, and quarters

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To determine the number of ways you can have $1.05 using only dimes, nickels, and quarters, we can use a systematic approach.

First, let's consider the possible number of quarters. Since quarters are worth 25 cents each, the maximum number of quarters we can have is 4 (25 cents * 4 = $1.00).

Now, let's calculate the remaining amount after considering the quarters. To have $1.05, we have 105 - 100 = 5 cents remaining.

Considering the remaining 5 cents, there are two possibilities: either we can use one nickel (worth 5 cents), or we can use 5 pennies (each worth 1 cent).

Let's further break down these possibilities:

Case 1: Using a nickel
If we use a nickel, we have 5 cents remaining. Since dimes are worth 10 cents each, we can use either 0, 1, 2, 3, 4, or 5 dimes (6 possibilities in this case).

Case 2: Using 5 pennies
If we use 5 pennies, we have no cents remaining. In this case, we have used all the remaining coins.

So, in total, we have 6 possibilities in Case 1 and 1 possibility in Case 2. Therefore, the total number of ways to have $1.05 using only dimes, nickels, and quarters is 6 + 1 = 7 ways.

How many nickles and dimes does it take to get to $1.05?

make a systematic listing of quarters, dimes and nickels to add up to $1.05, starting the the largest remaining possibility for each type of coin

Q D N
4 0 1
3 3 0
3 2 2
3 1 4
3 0 6
2 5 1
2 4 3
...
..
0 1 19
0 0 21