To solve this problem, we have to use the equivalence of each type in dollars.
Taking x, y and z as the number of nickels, dimes and quarters, we have that:

0.05 is the equivalence of one nickel in dollars, same for 0.1 and 0.25 with dimes and quarters respectively.
Now, we know that she has 2 more dimes than nickels:

And 4 more quarters than nickels:

We can use the expression for y and z in terms of x in the first equation to find the value of x (number of nickels):

Once we have found x, we can use it to find y and z using the equations we stated:

It means that Susan has 3 nickels, 5 dimes and 7 quarters.