rose counted her money and found that her 25 coins which were nickels, dimes, and quarters were worth $3.20. The number of dimes exceeded the number of nickels by 4. How many coins of each kind did she have?

Question

I know that the expression for nickles would be 5x, for dimes it would be
10x + 40, but i don't understand how to do the expression for quarters.....can someone help me with the answer

Answer 1

N = number of nickles
D = number of dimes = N+4
Q = number of quarters
= 25-N-D
= 25-N-(N+4)
= 21-(2N)

Add the coins to get $3.20
(N*$0.05) + (D*$0.10) + (Q*$0.25) = $3.20
Expressing D and Q in terms of N:
(N*$0.05) + ((N+4)*$0.10) + (21-2N)*$0.25=$3.20

Solve for N. Then plug N into the equations for D and Q

Answer 2

It is not clear what your x means, and where you came up with 10x + 40 for the value of the dimes. Let the numbers of nickels, dimes and quarters be N, D and Q.
5 N + 10 D + 25 Q = 320
D = N + 4
N + D + Q = 25

Now solve those three equations in three unknowns.

5 N + 10(N + 4) + 25 Q = 320
15 N + 25 Q = 280
2 N + 4 + Q = 25
Multiply that last equation by 25
50 N + 25 Q = 525
Now eliminate the Q
35 N = 245
N = 7
You do the rest