Question

In a group of cows and hens, the number of legs is 14 more than twice the number of heads. The number of cows is:
A) 5
B) 7
C) 10
D) 12
E) can't be determined

Answer 1

Hint: The given question will give an equation as per the given condition. The equation will be of the form of a linear equation of the two variables, we will assume the number of the cows and the hens and the total number of the heads will be the same as that of the sum of the number of the cows and hens.

Complete step by step answer:
Let us suppose that the number of the cows =\[x\]
Then the number of legs (of cows) = $ 4x $
No also let us suppose that the number of the hens= $ y $
Then the total number of the legs (of hens) = \[2y\]
So, the total number of the legs = $ 4x + 2y $
And since the number of the heads of the cows will be same as that of the number of the cows and also same for the hens, So the total number of the heads= $ x + y $
It is given in the question that the number of legs is 14 more than twice the number of heads, So the relation will give the following equation,
Total Number of legs= [{2(total number of the heads)} +14]
Mathematically,
 $ 4x + 2y = [2\{ x + y\} + 14] $
Now will solve this equation further,
  $ \Rightarrow 4x + 2y = 2x + 2y + 14 $
 $ \Rightarrow (4x - 2x) + (2y - 2y) = 14 $
 $ \Rightarrow (4x - 2x) = 14 $
 $ \Rightarrow 2x = 14 $
 $ \Rightarrow x = \dfrac{{14}}{2} $
 $ \Rightarrow x = 7 $
Hence the number of the cows in the given group of the cows and hen is $ 7 $ .
So, option (B) is the correct answer.

Note:
Here we have seen that in the equation the value of the coefficient of one of the variable (that is $ y $ , which stands for the number of the hens) is same on both sides of the equation so we just cancel out the value of that particular variable and the equation becomes like the linear equation in one variable. But if we don’t have the same value of the coefficient of any one of the variables then we would need two-equation to get the solution.