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Hi, this makes more CENTS :)
Sam has five more dimes than quarters and four fewer nickels than quarters
 and four fewer nickels than quarters
Quarters: x
Dimes: x+5
Nickels: x - 4
Question states***total of $4   0r 470 CENTS
CENTS makes sense
  25x + 10(x+5) + 5(x-4) = 470¢
     40x + 50 - 20 = 470
         40x = 440
           x = 11, number of quarters.   16 Dimes and 7 Nickels
and
  = 470¢   0r $4.70
 = 470¢   0r $4.70