Question

A man has some hens and cows. If the number of heads is 48 and the number of feet equals 140 then the numbers of hens will be?

Answer 1

Hint: To solve this question first of all assume two variables x and y as the number of cows and number of hens respectively. We know that both cow and hen have 1 head, the cow has 4 feet and the hen has 2 feet. Now using the given two conditions makes a linear equation of two variables and solves them finally to get the value of x and y.

Complete step-by-step solution:
This question is a type of linear equation in two variables, we will first make a linear equation and then solve them to get the required result.
Let the number of cows is x and the number of hens is y.
Given the total number of heads = 48.
Since each cow and hen have one head,
\[\Rightarrow x+y=48\] - (1)
Given that number of feet = 140.
Now a cow has 4 feet and a hen has 2 feet.
\[\Rightarrow \] Number of feets of all cows = 4x.
And the number of feets of all hens = 2y.
Now the total number of feet = number of feets of cow + number of feets of hens.
\[\Rightarrow \] Number of feet = 140
\[\Rightarrow 4x+2y=140\] - (2)
Now we will solve the two-equations (1) and equation (2).
Multiplying equation (1) by 2 and subtracting we get;
\[4x+2y=140\]
\[\underline{\begin{align}
  & 2x+2y=96 \\
 & -- \\
\end{align}}\]
\[2x=44\]
\[\Rightarrow x=\dfrac{44}{2}=22\]
Then the number of cows = x = 22.
Now we have from equation (1) we have,
\[x+y=48\]
\[\Rightarrow y=48-x\]
Substituting value of x = 22.
\[\begin{align}
  & \Rightarrow y=48-22 \\
 & \Rightarrow y=26 \\
\end{align}\]
Then the number of hens = y = 26. .

Note: The student can get confused by assuming both the variables are the same. Do not assume the same variable, the number of hens and the number of cows may differ so assume different variables. Also, be cautious while calculating the number of feet, the number of feet of a cow and of a hen is not the same. To avoid mistakes at this point.