Question

A person has certain number of cows and birds.They have 172 eyes and 344 legs.How many cows and birds does he have?

Answer 1

Solutions :-

Given :

A person has certain number of cows and birds.

They have 172 eyes and 344 legs.

Now,

Let the number of birds be x

And the number of cows be y

So, The equation will be

2x + 2y = 172 ........... (i)  

(both have two eyes)

2x + 4y = 344........... (ii)

(birds have two legs and Cows have four legs)

Here,

Let us eliminate the y term, and in order to eliminate the y term, equate the coefficient of y in both the equation.

(2x + 2y = 172)2 => 4x + 4y = 344 ........... (iii)

(2x + 4y = 344)1 => 2x + 4y = 344 ........... (iv)

Subtract equation (iii) from (iv)

(2x + 4y) - (4x + 4y) = 344 - 344

=> -2x = 0

=> x = 0

Substitute the value of x in Eq. (i) or Eq. (ii) to find the value of y. Substitute the value of x in the first equation, we have,

2x + 2y = 172

=> 2(0) + 2y = 172

=> 0 + 2y = 172

=> y = 172/2 = 86

Number of birds = x = 0

Number of cows = y = 86

Hence,

He has only 86 cows and no any birds.