Question

A farmer notes that in a field full of horses and chickens there are 35 heads and 98 feet. How many of each animal are there?

Answer 1

There are 14 horses and 21 chickens.

Explanation:

First, you have to make expression for horse and chicken. So we can let x be the number of horses and y will be the number of chickens. Next, given that the total number of feet for both animals is 98 so you have to make simultaneous equation :

`4x + 2y = 98`

( horse has 4 feet and chicken has 2 feet )

There are a total of 35 heads so the other equation will be :

`x + y = 35`

Lastly, you have to solve it :

`4x + 2y = 98`

`2(2x + y) = 98`

`2x + y = 49 - - - (1)`

`x + y = 35 - - - (2)`

`(1) - (2)`

`2x + y - x - y = 49 - 35`

`x = 14`

`substitute \: x = 14 \: into \: (2)`

`14 + y = 35`

`y = 35 - 14`

`y = 21`