N = number of nickles
D = number of dimes = N+4
Q = number of quarters
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
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
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