SOLUTION: can you help me find the formula for this problem? Laura found $2.15 in quarters and nickels in the bottom of her purse. there were seven fewer quarters than nickels. how many q

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Question 626124: can you help me find the formula for this problem?
Laura found $2.15 in quarters and nickels in the bottom of her purse. there were seven fewer quarters than nickels. how many quarters and nickels did she find?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

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