Question

There are cow and hen in the field by counting heads they are 52 the number of their legs is 176 how many cows are there

Answer 1

Answer:

The number of cows are 36 .

Step-by-step explanation:

"let no. of cows be x

and no. of hens be y

total cows and hens= 52

total no. of legs = 176

then,

according to question

x + y = 52 - equation (1)

[total cows + total hens = 52]

and

4x + 2y = 176 - equation (2)

[total no. of legs = 176

total no. of legs = 176 total legs of cows = 4*x

total legs of hens = 2*y]

on multiplying 4 in equation 1 and subtracting from equation 2, we get,

- 2y = -32

y = 16

putting y= 16 in equation 1

We get x= 36

hence no. of cows = 36

proof

36*4 + 16*2

144) + (32) = 176"

Answer 2

Given,

The total number of heads of cows and hens together$\[ = 52\]$

The total number of heads of cows and hens together$\[ = 176\]$

To find,

The number of cows.

Solution,

Assume that the number of cows and hens are x and y respectively.

Therefore,

$\[\begin{array}{l} \Rightarrow x + y = 52\\ \Rightarrow 4x + 2y = 176\end{array}\]$

Now,

$\[\begin{array}{l} \Rightarrow 4x + 2\left( {52 - x} \right) = 176\\ \Rightarrow 4x + 104 - 2x = 176\\ \Rightarrow 2x = 176 - 104\\ \Rightarrow 2x = 72\end{array}\]$

Solve further,

$\[\begin{array}{l} \Rightarrow x = \frac{{72}}{2}\\ \Rightarrow x = 36\end{array}\]$

Hence, the number of cows are$\[36\]$.