Nicole has a collection of 29 nickels and dimes worth $2.30. how many of each does she have?

You have two unknowns, so you need two equations to solve them. If n = the number of nickles, and d = the number of dimes, then we can say that n + d = 29. Furthermore, we can say that .05n + .1d = 2.30, i.e. the value of a nickel times the number of nickels plus the value of a dime times the number of dimes must equal the total value of the coins. We call this a system of equations. Both equations must work with correct answers. We can solve the system in more than one way. The easiest to understand is probably substitution. Given that n + d = 29, we can subtract d and say that n = 29 - d. Now we substitute (29 - d) into the other equation for n: .05(29-d) + .1d = 2.30        now distribute1.45 - .05d + .1d = 2.3        now combine like terms.05d = .85                           now divided = 17 dimes                      now use this with the first equation   n + 17 = 29  
n = 12

Hope this helps! Good luck!