A farm raises cows and chickens. The farmer has a total of 46 animals. One day he counts the legs of all his animals and realizes he has a total of 156 legs. How many chickens does the farmer have?

32 chickens

Step-by-step explanation:

Let

The number of cows = x

The number of chickens = y

A farm raises cows and chickens. The farmer has a total of 46 animals.

x + y= 46 Equation 1

x = 46 - y

Number of legs of chickens = 2

Number of legs of cows = 4

One day he counts the legs of all his animals and realizes he has a total of 156 legs.

Hence:

2x + 4y = 156 Equation 2

We substitute 46 - y for x in Equation 2

2(46 - y) + 4y = 156

92 - 2y + 4y = 156

- 2y + 4y = 156 - 92

2y = 64

y = 64/2

y = 32

Solving for x

x = 46 - y

x = 46 - 32

x = 14

The number of cows = x = 14 cows

The number of chickens = y = 32 chickens

Therefore, the number of chickens that the farmer has is 32 chickens

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