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There is an animal farm where chickens and cows live. all together, there are 96 heads and 230 legs. how many chickens and cows are there on the farm?

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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.

User Ivan Vergiliev
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