# of quarters # of nickels total value
x x+19 (cents)
------------------------------------------
0 19 95
1 20 125
2 21 155
...
10 29 395
11 30 425
Of course, in practice you wouldn't solve the problem by making a table; you could use basic algebra.
However, the table shows how I would solve the problem without algebra, using logical reasoning.
(1) The 19 "extra" nickels have a value of 95 cents.
(2) adding one more quarter and one more nickel (to keep the number of nickels 19 more than the number of quarters) adds 30 cents to the total.
(3) 95 cents is 330 cents short of the actual total of 425 cents. The number of times I have to add one quarter and one nickel to make those other 330 cents is 330/30 = 11.
So I have 11 quarters and 11+19 = 30 nickels