Question

A farmer was asked how many cows and chickens she has. The farmer replied, "between the cows and the chickens, there are 162 eyes and 270 feet." How many cows does she have? How many chickens does she have? (Note: chickens have 2 feet and cows have 4 feet.)

Answer 1

☀️ Solution:

We all know that,

• All animals have 2 eyes.
• All cows have 4 feet
• All hens have 2 feet

So, Let the no. of cows be x and chickens be y

According to question,

• Total number of eyes = 162

Framing equation,

⇛ Eyes of cows + Eyes of chickens = 162

⇛ 2x + 2y = 162

⇛ 2(x + y) = 162

⇛ x + y = 162/2 = 81 -----------(1)

According to question(Cond.-1)

• Total number of feet = 270

Framing equation,

⇛ Feet of cows + Feet of chickens = 270

⇛ 4x + 2y = 270

⇛ 2(2x + y) = 270

⇛ 2x + y = 135 ----------(2)

Subtracting eq.(1) from eq.(2),

⇛ 2x + y - (x + y) = 135 - 81

⇛ 2x + y - x - y = 54

⇛ x = 54

Putting value of x in eq.(1),

⇛ 54 + y = 81

⇛ y = 81 - 54

⇛ y = 27

⚘ So, Total number of animals,

• Number of cows = x = 54
• Number of chickens = y = 27

Hence, solved !$!$

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