A farm raises cows and chickens. The farmer has a total of 40 animals. One day he counts the legs of all his animals and realizes he has a total of 118 legs. How many cows does the farmer have?

The number of of cows and chickens the farmer has on his Farm is 19 and 21 respectively.

Given:

Total animals = 40

Total legs = 118

let

number of cows = x

number of chickens = y

x + y = 40 (1)

x + y = 40 (1)4x + 2y = 118 (2)

Multiply (1) by 2

2x + 2y = 80 (3)

4x + 2y = 118 (2)

subtract (3) from (2) to eliminate y

4x - 2x = 118 - 80

2x = 38

x = 38/2

x = 19

Recall,

x + y = 40

19 + y = 40

y = 40 - 19

y = 21

Therefore, the number of cows and chickens the farmer has on his Farm is 19 and 21 respectively.

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the farmer has 19 cows.

Step-by-step explanation:

Let x represent the number of cows that the farmer has.

Let y represent the number of chicken that the farmer has.

The farmer has a total of 40 animals. It means that

x + y = 40

A cow has 4 legs. A chicken has 2 legs. One day he counts the legs of all his animals and realizes he has a total of 118 legs. It means that

4x + 2y = 118- - - - - - - - 1

Substituting x = 40 - y into equation 1, it becomes

4(40 - y) + 2y = 118

160 - 4y + 2y = 118

- 4y + 2y = 118 - 160

- 2y = - 42

y = - 42/ - 2

y = 21

x = 40 - y = 40 - 21

x = 19

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