Robin has a collection of nickels, dimes, and quarters worth $57.50. She has 20 more dimes than nickels and twice as many quarters as dimes. How many coins of each kind does she have?

Let n be a number of nickels, d - dimes and q - quarters.

Then d=20+n and q=2d (*)

Since 25q+10d+5n=5750 -> 25(2d) + 10d + 5(d-20)=5750.

Simplifying, we get 65d-100=5750, 65d=5850, d = 90.

Substituting in (*) we get n=70, q=180.

Answer: Robin has 70 nickels, 90 dimes and 180 quarters.