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3 years ago

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A farmer was asked how many cows and chickens she has. The farmer replied, "between the cows and the chickens, there are 162 eye

s 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.)

1 answer:

Kazeer [188]3 years ago

8 0

<h2>☀️ <u>Solution</u><u>:</u></h2>

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 ! $!$

<u>━━━━━━━━━━━━━━━━━━━━</u>

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