Let x be the number of quarters. Since Nathan has twice as many nickels as quarters, the number of nickels is 2x. Multiply the number of each type of coin by the value of each type of coin, and add those products together to get 455 cents:
(x)(25) + (2x)(5) = 455
So, 25x + 10x = 455
35x = 455
Divide both sides by 35:
35x/35 = 455/35
You get: x = 13.
Since x was the number of quarters and 2x was the number of nickels, Nathan has 13 quarters and 26 nickels.
You can check the answer by verifying that (13*25) + (26*5) = 455.