text: 9 dimes\n(12 nickels, 16 quarters )\nThis is the answer, did you want the derivation as well?\nAnd why would you want to use only one variable?\n\nProof by example, using NO variables:\n9+12+16 = 37\n12*(.05) + 9*(.10) + 16*(.25) = 5.50\n16 = 12 + 4\n\nUsing one variable,\nX = nickels\n#quarters = X +4\n#dimes = 37 - X - (X+4) = 33 - 2X\nand\n5X + 25(X+4) + 10(33-2X) = 550\n10X + 430 = 550\n10X = 120\nX = 12 is the number of nickels\n#dimes = 33-2X = 33-24=9\n\n{But this isn't really using only one variable either.  Note that "#quarters" and "#dimes" above are really variables.  It is IMPOSSIBLE to solve with only one variable, because there are three unknowns-thus three variables are inherent in the problem.)