How many ways are there to make 14 cents?

Answer 1

The coins we know are:

1. A penny - 1 cent
2. A nickel - 5 cents
3. A dime - 10 cents
4. A quarter - 25 cents

Let x denote the number of pennies, y denote the number of nickels, z denote the number of dimes and w denote the number of quarter.

We can set up the expression this way:

x + 5y + 10z + 25w = 14

But since we want to make 14 cents, quarters are not considered to be the part of the combination, so we write:

x + 5y + 10z = 14

There is no quick way to work out this problem. All you need to do is to work by trials.

1. If we have y = 0 nickels and z = 1 dime, then the remaining choice is 4 pennies to make 14 cents.
2. If we have y = 2 nickels and z = 0 dimes, then the remaining choice is also 4 pennies.
3. If we have y = 1 nickel and z = 0 dimes, then the remaining choice is 9 pennies.
4. If y = z = 0 of these coins - nickels and dimes - , then we can make 14 cents by 14 pennies.

So there are 4 ways to form 14 cents.

Answer 2

16