How many different ways can you make change using 25-cents coin using dimes, nickels and pennies?

To find the different ways to make change using 25-cent coins (quarters) using dimes, nickels, and pennies, we can use a systematic approach called counting.

First, let's consider the highest-value coin we can use, which is a dime (10 cents). We can have either 0, 1, or 2 dimes in a 25-cent change.

If we have 0 dimes, we need to consider the next highest-value coin, which is a nickel (5 cents). The possible combinations of nickels and pennies are as follows:

- 0 nickels and 25 pennies
- 1 nickel and 20 pennies
- 2 nickels and 15 pennies
- 3 nickels and 10 pennies
- 4 nickels and 5 pennies
- 5 nickels and 0 pennies

Thus, there are 6 combinations when we have 0 dimes.

If we have 1 dime, we can fill the remaining 15 cents by using nickels and pennies in the following combinations:

- 0 nickels and 15 pennies
- 1 nickel and 10 pennies
- 2 nickels and 5 pennies
- 3 nickels and 0 pennies

Therefore, there are 4 combinations when we have 1 dime.

Lastly, if we have 2 dimes, we only need to consider the number of pennies needed to complete 5 cents since the maximum amount the pennies can sum up to is 5 cents. The combinations are:

- 0 pennies
- 1 penny
- 2 pennies
- 3 pennies
- 4 pennies
- 5 pennies

Thus, there are 6 combinations when we have 2 dimes.

Therefore, the total number of different ways we can make change using dimes, nickels, and pennies with a 25-cent coin is: 6 + 4 + 6 = 16.