Answer:
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
