In this problem, it is given that all the chickens and cows together have 96 heads and 230 legs. Since each chicken has 1 head and 2 legs, and each cow has 1 head and 4 legs, we can set up a system of two equations to solve the problem.
Let's denote the number of chickens as x and the number of cows as y.
From the total number of heads, we get our first equation:
x + y = 96
This is because each animal, regardless of being a chicken or cow, has one head.
From the total number of legs, we get our second equation:
2x + 4y = 230
This is because each chicken has 2 legs and each cow has 4 legs.
We can simplify the second equation by dividing each term by 2, to make it easier to work with:
x + 2y = 115
Now, we can solve this system of equations. If we subtract the first equation (x + y = 96) from our modified second equation (x + 2y = 115), we are left with:
115 - 96 = 2y - y
This simplifies to:
19 = y
So, there are 19 cows on the farm.
Substitute y = 19 into the first equation (x + y = 96), we get:
x + 19 = 96
Subtract 19 from both sides to solve for x:
x = 96 - 19 = 77
So, there are 77 chickens on the farm.
In summary, there are 77 chickens and 19 cows on the farm.