Question

There is a group of cows and chickens. The number of legs was 14 more than twice the number of heads. The number of cows is
A. 5
B. 8
C. 7
D. 4

Answer 1

Hint: The cows have four legs each, while the chickens have two. Assume there are x number of cows and y number of chickens. Now, with the help of the given data form an equation and solve for the value of x.

Complete step-by-step answer:
Assume there are x number of cows and y number of chickens.
∴ total number of heads is \[x + y\]
Now, the cows have four legs each, while the chickens have two.
Therefore, total number of legs is $4x + 2y$
Given, the number of legs is 14 more than twice the number of heads, i.e.,
 $
  4x + 2y = 2(x + y) + 14 \\
   \Rightarrow 4x + 2y = 2x + 2y + 14 \\
   \Rightarrow 2x = 14 \\
   \Rightarrow x = 7 \\
 $
∴ the number of cows is 7.
Therefore option (C) is correct.


Note: Here we have only one linear equation in two variables, as one of the variable got cancelled, hence we could easily find the other variable, but not all the questions will have the same type, if we have one linear equation in 2 variables, there can be infinite possible solutions to that if not variable gets cancelled.