The farmer raises rabbits and ostriches. There are 200 heads and 700 paws on the farm.

The farmer raises rabbits and ostriches. There are 200 heads and 700 paws on the farm. How many rabbits and how many ostriches?

Let the number of rabbits that the farmer raise is x, and the number of ostriches is equal to y.

Thus, all of them on the farm will be:

x + y = 200.

Since a rabbit has 4 legs, and an ostrich has 2, then the total number of legs will be:

4 * x + 2 * y = 700.

Express the unknown number of rabbits x from the first equation.

x = 200 – y.

We substitute in the second.

4 * (200 – y) + 2 * y = 700.

800 – 4 * y + 2 * y = 700.

2 * y = 100.

y = 100/2 = 50 ostriches.

x = 200 – 50 = 150 rabbits.

Answer: 150 rabbits and 50 ostriches.