Your error is in adding coins and getting dollars.
You can't do that.
A collection of nickels and quarters is worth 4.65.
That translates as the MONEY equation
($.05)n + ($.25)q = $4.65
There are 3 more nickels than quarters.
That translates as the COIN equation:
n = q + 3
So the system is
.05n + .25q = 4.65
n = q + 3
You can simplify the first equation by clearing of decimals
by multiplying through by 100
5n + 25q = 465
n = q + 3
Substitute q + 3 for n in the first equation:
5n + 25q = 465
5(q + 3) + 25q = 465
5q + 15 + 25q = 465
30q + 15 = 465
30q = 450
q = 15
Substitute 15 for q in
n = q + 3
n = 15 + 3
n = 18
So there were 18 nickels and 15 quarters.
Edwin