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

Answer:

There are 14 horses and 21 chickens.

Step-by-step 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 :

$4x + 2y = 98$

$2(2x + y) = 98$

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

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

$(1) - (2)$

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

$x = 14$

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

$14 + y = 35$

$y = 35 - 14$

$y = 21$