Hi, 

 total of 50 coins       

Let x and (50-x) represent the number of quarters and nickels respectively

question states***

 25x + 5(50-x) = 410  cents

          20x = 160

            x = 8, the number of quarters.  Nickels number 42.    (50-8)



CHECKING our Answer

   8*25 + 5*42 = 200 + 210 = 410 cents = $4.10 

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