Final answer:
Calculating the different ways to make change for a quarter using pennies, nickels, and dimes involves identifying all possible combinations of these coins that add up to 25 cents. After systematically exploring the possibilities, we find there are 12 unique ways to make change for a quarter. This problem demonstrates understanding of coin values and arithmetic, which are part of middle school mathematics.
Step-by-step explanation:
To determine how many ways you can make change for a quarter using only pennies, nickels, and dimes, we'll look at the possible combinations of these coins that equal 25 cents. Since a quarter is equivalent to 25 pennies, we can start with this as one way. From there, we'll systematically explore combinations by introducing nickels and dimes and reducing the number of pennies correspondingly.
- 25 pennies = 25 cents
- 5 pennies and 2 dimes = 25 cents
- 10 pennies and 1 nickel and 1 dime = 25 cents
- 15 pennies and 1 nickel = 25 cents (2 nickels and 1 dime work too)
- 10 pennies and 3 nickels = 25 cents
- 5 pennies and 4 nickels = 25 cents
- 5 dimes = 25 cents
- 20 pennies and 1 nickel = 25 cents
- 20 pennies and 1 dime = 25 cents
By continuing this process, we'll cover all the possibilities, being careful not to duplicate combinations: for example, 1 dime can replace two nickels. Going through all the combinations, we find there are actually 12 ways to make change for a quarter. This exercise requires understanding of coin values and basic arithmetic operations. It's important to remember that both these skills and familiarity with monetary units, such as cents and dollars, are typically taught in middle school mathematics.