Let N = the number of Nickels

there were seven fewer quarters than nickels.

No. of Quarters = No. of Nickels - 7

No. of Quarters = N - 7


          number of coins | Value of each type coin | Value of coins
Nickels          N        |          $0.05          |     $0.05N   
Quarters        N-7       |          $0.25          |   $0.25(N-7)
--------------------------------------------------------------------
                                               Total|   $2.15


                            $0.05N + $0.25(N-7) = $2.15

Remove the dollar marks and move the decimals 2 places right:

                                   5N + 25(N-7) = 215

Divide through by 5

                                    N +  5(N-7) = 43
                                    N + 5N - 35 = 43
                                        6N - 35 = 43
                                             6N = 78
                                              N = 13

So there are 13 nickels, and 7 fewer quarters makes 13-7 = 6 quarters.

Checking: 13 nickels are worth 65 cents or $0.65. 6 quarters is $1.50. 
Adding those does indeed give $2.15

Edwin