Question

Out of herd of camels, $\frac{7}{2}$ times the square root of the total are grazing in the field. Two remaining are sitting in the field. Find the total number of camels.

Answer 1

Step 1: Determining the quadratic equation in $x$

Let the total number of camels be $x^2$.

Since it is given that, out of the herd of camels, $\frac{7}{2}$times the square root of the total are grazing in the field and the remaining two are sitting in the field.

$\begin{array}{rcl}\therefore \frac{7}{2}\sqrt{x^2}+2& =& x^2\\ & \Rightarrow & 2x^2-7x-4=0\end{array}$

Step 2: Determining the total number of camels $\left(x^2\right)$

By using the factorization method,

$$\begin{gathered} \Rightarrow 2x^2-7x-4=0 \\ \Rightarrow 2x-8x+1-4=0 \\ \Rightarrow 2x\left(x-4\right)+1\left(x-4\right)=0 \\ \Rightarrow (x-4)(2x-1)=0 \\ \Rightarrow x=-\frac{1}{2},4 \end{gathered}$$

Here, $x=-\frac{1}{2}$ is not considerable.

So, we have $x^2=4^2=16$

Hence, the total number of camels is $16$.