How many different ways are there to make 30 cents with pennies nickels dimes or quarters?

There is 1 way to make 30 cents using only pennies. (i.e. 30 pennies = 30 cents)

There is 1 way to make 30 cents using only nickels. (i.e. 6 nickels = 30 cents)

There is 1 way to make 30 cents using only dimes. (i.e. 3 dimes = 30 cents)

There are 5 ways to make 30 cents using only pennies and nickels. (i.e. 25 pennies + 1 nickel = 30 cents, 20 pennies + 2 nickels = 30 cents . . . )

There are 2 ways of making 30 cents using only pennies and dimes. (i.e. 20 pennies + 1 dime = 30 cents, 10 pennies + 2 dimes = 30 cents)

There is 1 way of making 30 cents using only pennies and quarters. (i.e. 5 pennies + 1 quarter = 30 cents)

There are 2 ways of making 30 cents using only nickels and dimes. (i.e. 4 nickels + 1 dime = 30 cents, 2 nickels + 2 dimes = 30 cents)

There is 1 way of making 30 cents using only nickels and quarters. (i.e. 1 nickel + 1 quarter = 30 cents)

There are 4 ways to make 30 cents using only pennies, nickels and dimes. (i.e. 15 pennies + 1 nickel + 1 dime = 30 cents, 10 pennies + 2 nickels + 1 dime = 30 cents . . . )

Adding all the possible combinations therefore, there are 18 different ways are there to make 30 cents with pennies nickels dimes or quarters.

There are 18 different ways to make 30 cents with pennies, nickels, dimes or quarters.

Solution:

We know that,

1 nickel = 5 cents

1 penny = 1 cent

1 dime = 10 cents

1 quarter = 25 cents

Now, number of ways are -

1 way to make 30 cents using only pennies -

30 pennies = 30 cents

1 way to make 30 cents using only nickels -

6 nickels = 30 cents

1 way to make 30 cents using only dimes -

3 dimes = 30 cents

5 ways to make 30 cents using only pennies and nickels -

25 pennies + 1 nickel = 30 cents; 20 pennies + 2 nickels = 30 cents and so on.

2 ways of making 30 cents using only pennies and dimes -

20 pennies + 1 dime = 30 cents and 10 pennies + 2 dimes = 30 cents

1 way of making 30 cents using only pennies and quarters

5 pennies + 1 quarter = 30 cents

2 ways of making 30 cents using only nickels and dimes -

4 nickels + 1 dime = 30 cents, 2 nickels + 2 dimes = 30 cents

1 way of making 30 cents using only nickels and quarters

1 nickel + 1 quarter = 30 cents

4 ways to make 30 cents using only pennies, nickels and dimes -

15 pennies + 1 nickel + 1 dime = 30 cents ; 10 pennies + 2 nickels + 1 dime = 30 cents and so on.

There are 18 different ways to make 30 cents with pennies, nickels, dimes or quarters.

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