Question

A barn holds rabbits and pheasant only. There are 35 heads and 98 legs in the yard. How many rabbits and pheasant are in the yard

Answer 1

There are 14 rabbits and 21 pheasants in the yard.

Explanation:

Since we don't know the number of animals, lets introduce two variables: the number of rabbits are x and the number of pheasants are y.

Rabbits have 4 feet, so the equation to find the total feet of all rabbit would be 4x.

Pheasants have 2 feet, so the equation to find all of their feet would be 2y.

The total number of heads is 35. Since there are x rabbits and y pheasants, and all of them have 1 head, we get this:

`x + y = 35`

The total number of legs is 98. Since all rabbits have a total of 4x legs and all pheasants have 2y legs, we get this:

`4x + 2y = 98`

If we use them together, we get a linear equation, which we can solve for x:

`x + y = 35 \: \: ( * - 2)\\ 4x + 2y = 98`

`\: \: \: \: \: \: - 2x - 2y = - 70 \\ + \: \: \: \: \: \: 4x + 2y = 98`

`2x = 28 \\ x = 14`

So, there are 14 rabbits. We can find the number of pheasants by diving 14 heads from the total of 35 heads:

`35 - 14 = y \\ y = 21`

and so we have 21 pheasants.

Answer 2

Answer:14 rabbits and 20pheasants

Step-by-step explanation: pheasants are birds and they have 2 leg each,rabbit are mammals and they have for legs..now if there are 35 animals and 98 legs in the barn it means there are 15 rabbits

14×4legs=56legs(rabbit)

20×2legs=40(pheasants)