a group of ducks and cows are in a field they have a total of 65 heads and 226 legs how many ducks are in the field

Question

A group of ducks and cows are in the field they have a total of 65 heads and 226 legs how many ducks are in the field

Answer 1

Each duck has  1 head and 2 legs.  Each cow has 1 head and 4 legs.

 

Let x = number of ducks

     y = number of cows

 

Then 1x + 1y = 65  ← heads

        2x + 4y = 226  ← legs

 

Multiply the first equation by -2 and leave the second equation as is

 

       -2x - 2y = -130

        2x +4y = 226

 

Add the equations to obtain 2y = 96    So, y = 48

                                                           x =  17

 

There are 17 ducks and 48 cows.