text: algebra question, i'll reward 10 points to answer? jo has 37 coins (all nickels, dimes, and quarters) worth $5.50. she has 4 more quarters than nickels. how many dimes does jo have? use only one variable 9 dimes (12 nickels, 16 quarters ) this is the answer, did you want the derivation as well? and why would you want to use only one variable?  proof by example, using no variables: 9+12+16 = 37 12*(.05) + 9*(.10) + 16*(.25) = 5.50 16 = 12 + 4  using one variable, x = nickels #quarters = x +4 #dimes = 37 - x - (x+4) = 33 - 2x and 5x + 25(x+4) + 10(33-2x) = 550 10x + 430 = 550 10x = 120 x = 12 is the number of nickels #dimes = 33-2x = 33-24=9  {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.)