SOLUTION: There are 19 animals in the field. Some are goats and some are ducks. There are 72 legs in all. How many of each animal are in the field?

Let x be the number of goats;  then the number of ducks is (19-x).


There is no need to remind that the ducs have two legs, while the goats have four legs.


So we write an equation for the total of legs


    4x + 2*(19-x) = 72.


Simplify and find x


    4x + 38 - 2x = 72

    4x - 2x = 72 - 38

      2x    =   34

       x    =   34/2 = 17.


ANSWER.  There are 17 goats and 19-17 = 2 ducks.


CHECK.   17*4 + 2*2 = 68 + 4 = 72  total legs.   ! Correct !