Roxanne's Coins

32) Roxanne had 39 coins (quarters and dimes) that totaled $7.80.  How many
of each coin did she have?

        x = quarters
        y = dimes

        x + y = 39 (Our first equation deals with the number of coins.)

        25x + 10y = 780 (These amounts are in pennies.)

        -10x -10y = -390  (We multiplied the top equation by -10, so that
                          we'll be able to cancel out a variable when adding.)

        -10x -10y = -390
         25x +10y =  780
         ---------------
         15x  =     390

           x = 26  (We divided both sides by 15 to find the value of x.)

           We will now plug the value of x (26) into the equation above to
           determine the value of y:

           26 + y  = 39

           y = 13  (We subtracted 26 from both sides to isolate the variable
                   y on one side of the equal sign and see its value on the
                   other.)

           Now that we know the value for both variables, we can double-check
           our work:

           26 quarters = $6.50
           13 dimes    = $1.30
           -------------------
           39 coins      $7.80