Question

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

Answer 1

Hint: We are given some information using which we have to create a system of linear equations in two variables. We should be aware about the fact that the number of heads of both deer and human is 1. And the number of legs of a human is 2, whereas the number of legs of a deer is 4. Using this we will assume the number of deer and humans to be some variables and we will create two equations out of that and then we will solve those equations.

Complete step by step answer:
We know that the number of heads of a deer is 1 and the number of legs of a deer is 4. So, if we assume there are $t$ deer then the number of heads of $t$ deer will be $t$ and the number of legs will be $4t$. We will do the same with human visitors too.
So, assume that the number of human visitors is $x$ and the number of deer is $y$.
Then, the total number of heads of both human visitors and deer will be $x+y$. And according to question, that number is equal to 39, so the first equation becomes:
$x+y=39$..................$\left(A\right)$
And the total number of legs are 132 so, the second equation becomes:
$2x+4y=132$
Divide this equation by 2;
$x+2y=66$
Subtract equation $\left(A\right)$ from this we get:
y=66-39=27
Put this in $\left(A\right)$:
$x+27=39$
$\implies x=12$
Hence, the number of human visitors is 12 and the number of deer is 27.

Note: Make sure that while calculating the number of total legs you multiply by the number of legs of one deer and one human respectively. Moreover, while solving the equations, try not make any calculation mistakes otherwise that would lead to an invalid result.