Final answer:
There are 12 different ways to make change for a quarter using U.S. coins, which includes combinations of quarters, dimes, nickels, and pennies.
Step-by-step explanation:
When considering how to make change for a quarter, which is 25 cents, you need to look at the denominations of U.S. coins available: pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents). You can start by picturing the various combinations you could make using those coins to add up to 25 cents. For example, you could have one quarter, two dimes one nickel, and so on. By systematically going through all the different combinations, you would find that there are 12 different ways to make change for a quarter:
- 1 quarter
- 2 dimes, 1 nickel
- 2 dimes, 5 pennies
- 1 dime, 3 nickels
- 1 dime, 2 nickels, 5 pennies
- 1 dime, 1 nickel, 10 pennies
- 1 dime, 15 pennies
- 5 nickels
- 4 nickels, 5 pennies
- 3 nickels, 10 pennies
- 2 nickels, 15 pennies
- 1 nickel, 20 pennies
How you approach a problem in math can often be back-calculated from something you already know. If you understand fractions and probability, you can apply these concepts to other scenarios, such as determining the ways to make change or the outcomes of coin tosses.