Question

On a farm, there are chickens and goats. Each chicken has 2 legs and each goat has 4 legs. The farmer counted 50 heads and 128 legs. Express, in terms of x, the number of goats on the farm.

Answer 1

Explanation:

Let the Number of Goats in the Farm be : X

Let the Number of Chickens in the Farm be : Y

We know that Each Chicken has One Head and Each Goat has One Head

Given : The Total Number of Heads = 50

⇒ The Sum of Goats and Chickens in the Farm is Equal to 50

⇒ X + Y = 50 ------------------ [1]

We know that Each Chicken has 2 Legs and Each Goat has 4 Legs

Given the Total Number of Legs in the Farm = 128

⇒ 2 × Number of Chicken + 4 × Number of Goat = 128

⇒ 4X + 2Y = 128

⇒ 2(2X + Y) = 128

⇒

⇒ 2X + Y = 64 ------------------- [2]

Subtracting Equation [1] from Equation [2] , We get :

⇒ (2X + Y) - (X + Y) = (64 - 50)

⇒ 2X + Y - X - Y = 14

⇒ X = 14

⇒ The Number of Goats in the Farm are : 14

Answer 2

Let the Number of Goats in the Farm be : X

Let the Number of Chickens in the Farm be : Y

We know that Each Chicken has One Head and Each Goat has One Head

Given : The Total Number of Heads = 50

⇒ The Sum of Goats and Chickens in the Farm is Equal to 50

⇒ X + Y = 50 ------------------ [1]

We know that Each Chicken has 2 Legs and Each Goat has 4 Legs

Given the Total Number of Legs in the Farm = 128

⇒ 2 × Number of Chicken + 4 × Number of Goat = 128

⇒ 4X + 2Y = 128

⇒ 2(2X + Y) = 128

⇒
`2X + Y = (128)/(2)`

⇒ 2X + Y = 64 ------------------- [2]

Subtracting Equation [1] from Equation [2] , We get :

⇒ (2X + Y) - (X + Y) = (64 - 50)

⇒ 2X + Y - X - Y = 14

⇒ X = 14

⇒ The Number of Goats in the Farm are : 14