Hi,

same number of pennies and nickels, number of dimes is 5 more than the number of nickels

Let x represent the number of pennies and nickels 

and (x+5)represent the number of dimes

Question states***CENTS makes sense

 x + 5x + 10(x+5) = 290 CENTS

Solving for x

       16x = 240

         x = 15, number of pennies and the number of nickels.  

                there were 20 Dimes   (15+5)



CHECKING our Answer***

  15 + 5*15 + 200 = 290 CENTS OR $2.90 

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