Question

How many different ways can you make change for a 50-cent coin using nickels and dimes?

Answer 1

There are 6 different ways to make change for a 50-cent coin using only nickels and dimes, ranging from 10 nickels and no dimes to no nickels and 5 dimes.

Step-by-step explanation:

We need to determine the different ways to make change for a 50-cent coin using just nickels (5 cents) and dimes (10 cents). First, note that the maximum number of nickels that can be used is 10 (since 10 nickels would make 50 cents), and the maximum number of dimes is 5 (since 5 dimes would make 50 cents).

To find the total number of ways we can combine nickels and dimes to make 50 cents, we can create combinations that add up to 50 cents, starting with 0 dimes and incrementing the count of dimes while decreasing the count of nickels accordingly.

1. No dimes: 10 nickels = 50 cents.
2. One dime: 8 nickels + 1 dime = 50 cents
3. Two dimes: 6 nickels + 2 dimes = 50 cents
4. Three dimes: 4 nickels + 3 dimes = 50 cents
5. Four dimes: 2 nickels + 4 dimes = 50 cents
6. Five dimes: 0 nickels + 5 dimes = 50 cents

Each of these combinations represents a different way to make change for a 50-cent coin, so there are 6 different ways to make change for a 50-cent coin using nickels and dimes.

Answer 2

10 ways

Step-by-step explanation:

When we do not use any quarters, we can use 0,1,2,3,4, or 5 dimes only

and the rest of the 50 cents, if any, in nickels. That's 6 ways.

If we use only 1 quarter, then we can use 0,1, or 2 dimes, and

the rest is nickels. That is 3 more ways.

if We can use 2 quarters. That's 1 more way.

So together there are 6+3+1 = 10 ways. in total

hope you got the point.