Question

A farm raises pigs and chickens. The farmer has a total of 66 animals. One day he counts the legs of all his animals and realizes he has a total of 174 legs. How many chickens does the farmer have? Please help me this is to hard!

Answer 1

The farmer has 45 chickens.

Explanation:

Let x = number of chickens

Let (66-x) = number of pigs

Pigs have 4 legs = 4(66 - x)

Chickens have 2 legs = 2x

4(66-x) + 2x = 174

• distribute the 4 to the bracket

= 264 - 4x + 2x = 174

• move the x together

= -4x + 2x = 174 - 264

• add together

= -2x = -90

• divide both sides be -2

= x = 45 <-- number of chickens

number of pigs: 66 - x

66 - 45 = 21

just to check!

(45 x 2) + (21 x 4) = 174

Answer 2

The farmer has 45 chickens

Explanation:

Let the number of pigs = p

Let the number of chickens = c

Total animals = 66

p + c = 66 ---------------------(I)

c = 66 - p

A pig has 4 legs. so 'p' number of pigs has p*4 = 4p legs

A chicken has 2 legs. so 'c' number of pigs has c*2 = 2c legs

Total legs = 174

4p + 2c = 174 --------------------(II)

Substitute c = 66 -p in equation (II)

4p + 2(66 - p) = 174

4p + 2*66 - 2*p = 174

4p + 132 - 2p = 174

4p - 2p + 132 = 174 {Combine like terms}

2p + 132 = 174 {Subtract 132 from both sides}

2p = 174 - 132

2p = 42 {Divide both sides by 2}

p = 42/2

p = 21

Plugin p =21 in equation (I)

21 + c = 66

c = 66 -21

c = 45

The farmer has 45 chickens