There are 36 coins consist of nickels, dimes, and quarters. There are three fewer quarters than nickels and six more dimes than quarters. How many of each kind of coin is there?

Number of Nickels is 12

Number of Dimes is 9

Number of Quarters is 15

Step-by-step explanation:

Given that there are a total of 36 coins, which consists of nickels, dimes, and quarters.

That is, when we sum the numbers of nickels, dimes, and quarters, we have 36.

Let number of nickels be N

Let number of dimes be D

Let number of quarters be Q

Then

N + D + Q = 36 ... (1)

- There are three fewer quarters than nickels.

This implies that

N = Q - 3 ... (2)

Or

Q = N + 3 ... (3)

- There are six more dimes than quarters.

This implies that

Q = D + 6 ... (4)

Comparing (3) with (4), we see that

N + 3 = D + 6

N - D = 6 - 3

N - D = 3 ... (5)

Using (3) in (1)

N + D + (N + 3) = 36

2N + D = 36 - 3

2N + D = 33 ... (6)

Solving (5) and (6) simultaneously

From (5) : D = N - 3

From (6) : D = 33 - 2N

=> N - 3 = 33 - 2N

N + 2N = 33 + 3

3N = 36

N = 36/3 = 12 ... (7)

Using (7) in (6)

2 (12) + D = 33

24 + D = 33

D = 33 - 24

D = 9 ... (8)

Using (7) and (8) in (1)

12 + 9 + Q = 36

21 + Q = 36

Q = 36 - 21 = 15 ... (9)

Therefore,

Number of Nickels, N = 12

Number of Dimes, D = 9

Number of Quarters, Q = 15