My piggy bank is overflowing, so I have been sorting coins for the past few days. I only save quarters (25¢), dimes (10¢), and nickels (5¢). As you can see from the photo, I have LOTS more quarters than dimes and more dimes than nickels. That got me thinking about the least amount of coins required (using only quarters, dimes, and nickels - no pennies) to make change from 5 cents to 95 cents.
The following possible combinations illustrate why I have more quarters than dimes and more dimes than nickels. In short, there are 8 ways to receive a nickel as change, 16 ways to receive a dime, and 30 ways to receive a quarter. However, there are numerous ways to extend this math problem. What math activities can you create with my piggy bank challenge?