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

Required Solution :–

★ The number of deer = 72 ★

Given:

• Half of a herd of deer are grazing in the field and three-fourths of the remaining are playing.

• The rest 9 are drinking water from the pond.

To calculate:

• The number of deer in the herd.

Calculation:

Let us assume the number of deer in the herd as x.

So, as the question states :

›» Half of a herd of deer are grazing in the field.

$\rm \red {\implies Number \: of \: those \: who \: are\: grazing = \dfrac{x}{2} }$

Now,

$\implies$ Remaining deer = $\sf {x -\dfrac{x}{2}}$

$\implies$ Remaining deer = $\sf {\dfrac{2x-x}{2}}$

$\rm \red {\implies Remaining \: deer = \dfrac{x}{2}}$

Also, as the question states :

›» Three-fourths of the remaining are playing.

$\implies$ Number of those who are playing = $\sf {\dfrac{3}{4} \: of \: \dfrac{x}{2} }$

$\implies$ Number of those who are playing = $\sf {\dfrac{3}{4} \times \dfrac{x}{2} }$

$\implies$ Number of those who are playing = $\sf {\dfrac{3 \times x}{4 \times 2} }$

$\rm \red {\implies Number \: of \: those \: who \: are\: playing = \dfrac{3x}{8} }$

And the other 9 deer are drinking, thus

$\sf { Total \: number \: of \: deer = \dfrac{x}{2} + \dfrac{3x}{8} + 9 }$

→$\sf { x = \dfrac{x}{2} + \dfrac{3x}{8} + 9 }$

→$\sf { x = \dfrac{4x+3x+72}{8} }$

→$\sf { x = \dfrac{7x+72}{8} }$

→$\sf { x \times 8 = 7x+72 }$

→$\sf { 8x = 7x+72 }$

→$\sf { 8x - 7x = 72 }$

→$\sf { x = 72 }$

$\rm \green{ \longrightarrow Total \: number \: of \: deer = 72 }$

Therefore, the number of deer in the herd is 72 .