Question

Half of a herd of deer are grazing in the field and three fourths of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.​

Answer 1

Step-by-step explanation:

Let the total no of deer be x

So, we have

x−(

2

1

x+

4

3

×

2

1

x)=9

x−(

2

1

x+

8

3

x)=9

x−

8

7

x=9

8

1

x=9;

Thus, x=72 deer in the herd

Answer 2

Answer:

Total number of deer is 72

Explanation:

Let's say the total number of deer in the herd is x

Now,

$\rm = \dfrac{1}{2} \: of \: x \: are \: grazing$

$\rm = \dfrac{x}{2}$

Remains :

$\rm = x - \dfrac{x}{2}$

$\rm = \dfrac{x}{2}$

And also,

$\rm = \dfrac{3}{4} \: of \: \dfrac{x}{2} \: are \: playing \: nearby$

$\rm = \dfrac{3x}{8}$

${\underline{ \boldsymbol{According \: to \: the \: question \: :}}}$

Rest of the 9 are drinking water,

Then,

$\rm \implies x - \bigg( \dfrac{x}{2} + \dfrac{3x}{8} \bigg) = 9$

On solving further,

$\rm \implies x - \bigg(\dfrac{4x + 3x}{8} \bigg) = 9$

$\rm \implies x - \bigg(\dfrac{7x}{8} \bigg) = 9$

$\rm \implies x - \dfrac{7x}{8} = 9$

$\rm \implies \dfrac{8x - 7x}{8} = 9$

$\rm \implies \dfrac{x}{8} = 9$

$\rm \implies {x} = 9 \times 8$

$\rm \implies {x} = 72$

∴ Total number of deer is 72