Answer:
There are 14 cows and 68 Chicken in the farm.
Step-by-step explanation:
A Cow has 4 legs
Chicken has 2 legs.
Lets take there [tex]x[/tex] chickens AND,
there are [tex]y[/tex] number of Cows.
Now we can write two equations for the number of heads and legs.
For the number of heads we can write,
[tex]x+y=82[/tex] <--------- 1st equation
For the number of legs we can write,
[tex]2x+4y=192[/tex] <------ 2nd equation
We can now solve the simultaneous equations to find [tex]x[/tex] and [tex]y[/tex]
Multiply 1st equation by 2 and deduct it from 2nd equation to remove [tex]x[/tex]
⇒[tex]2x+4y-2*(x+y)=192-164[/tex]
⇒[tex]2x+4y-2x-2y)=112-164[/tex]
⇒[tex]2y=28[/tex]
⇒[tex]y=14[/tex]
Therefore, there are 14 cows in the farm.
Now we can substitute the [tex]y[/tex] value to the 1st equation and find [tex]x[/tex] value.
[tex]x+14=82[/tex]
[tex]x=68[/tex]
Therefore, there are 68 chickens in the farm.
