Question

At a certain time in a deer park, the number of heads and number of legs of deer and human visitors was counted and it was found that there were $39$ heads and $132$ legs. Find the number of deers and human visitors in the park.

Answer 1

Step 1: Form equations using given data.

Let $x$ be the total number of heads of deer and $y$be the total number of heads of human visitors.
therefore, $x+y=39$---------------------------$\left(i\right)$
As $1$ deer has $4$ legs and $1$ head & $1$ human visitor has $2$ legs and $1$ head. we get,
$4x+2y=132$--------------------------$\left(ii\right)$

Step 2: Solve the obtained equations.

Solving equation$\left(i\right)$and $\left(ii\right)$

On multiply by $4$ in equation $\left(i\right)$we have

$4x+4y=156$--------------------------$\left(iii\right)$

On subtracting the equation $\left(ii\right)$ from $\left(iii\right)$we have,

$$\begin{gathered} 2y=24 \\ \Rightarrow y=12 \end{gathered}$$

In putting $y=12$ in the equation $\left(i\right)$we have ,

$$\begin{gathered} x+12=39 \\ \Rightarrow x=27 \end{gathered}$$

Hence, the total number of visitors $=12$ and the total number of deers $=27$ .