Question

Out of a group of deer, 7/2 times the square root the total number are grazing grass and remaining two are playing . Find the total number of deer in the group.

Answer 1

The total number of deer in the group is 16.

Step-by-step explanation:

Given:

Let us assume that the total number of deer is x

Here it is given that out of a group of deer, $\frac{7}{2} \times \sqrt{x}$ the total number are grazing grass and remaining two are playing.

Also it is given that number of deer grazing grass = $\frac{7}{2} \times \sqrt{x}$

Remaining deer who are playing = 2

Therefore  total number of deer in the group will be,

$x= \frac{7}{2} \sqrt{x}+2$

$x-2= \frac{7}{2} \sqrt{x}$

$2(x-2)=7\sqrt{x}$

So, squaring both the sides, we get

$[2(x-2)]^2=[7\sqrt{x}]^2$

$4(x^2-4x+4)=49x$

$4x^2-16x+16=49x$

$4x^2-16x-49x+16=0$

$4x^2-65x+16=0$

$4x^2-64x-x+16=0$

4x(x-16)-1(x-16) = 0

(x-16)(4x-1) = 0

x - 16 = 0 or 4x-1 = 0

x = 16 or $x=\frac{1}{4}$ [It is not possible]

Therefore, x = 16

The total number of deer in the group is 16.