Call x the number of nickles that she has.
Then the number of quarters is twice x = 2x
And the number of dimes is three times x = 3x.
So, the total number of coins is x + 2x + 3x = 240
=> 6x = 240
=> x = 240 / 6
=> x = 40
=> Number of nickels = x = 40
Number of quarters = 2x = 80
Number of dimes = 3x = 120
Verification: 40 + 80 + 120 = 240
Answer: nickles 40, quarters 80, and dimes 120.