Answer:
There are 16 cows and 24 chickens 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=40[/tex] <--------- 1st equation
For the number of legs we can write,
[tex]2x+4y=112[/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)=112-80[/tex]
⇒[tex]2x+4y-2x-2y)=112-80[/tex]
⇒[tex]2y=32[/tex]
⇒[tex]y=16[/tex]
Therefore, there are 16 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+16=40[/tex]
[tex]x=24[/tex]
Therefore, there are 24 chickens in the farm.
