I'll assume you don't mean to use pennies or half dollars

then let q = the number of quarters
     let d = the number of dimes
    then 3d = the number of nickels.

Then there is a "coin equation" and a "money equation":


The "coin" equation is

  +  +  = 85


The "money" equation is:

 +  +  = $6.25



Simplify:

Simplify some more:

Multiply the second one through by 100 to clear of decimals:

Divide the second equation through by 25

  
Solve that and get q=5 and d=20

So there are 5 quarters, 20 dimes, and since there are 3d nickels,
there are 3(20) or 60 nickels.

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If you allow pennies there are two more solutions:

12 quarters, 12 dimes, 36 nickels and 25 pennies

19 quarters, 4 dimes, 12 nickels and 50 pennies.

But there are no solutions using half dollars.

Edwin