Question

8. 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.

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Answer 1

Let the total number of deer in the herd be x.

According to question, x= x/2 + 3/4 × (x-x/2) +9

⇒ x = x/2 + 3/4 [(2x-x)/2]+ 9

⇒ x = (x/2 +3/4) × (x/2 +9)

⇒ x= (x/2) + (3/8)x +9

⇒ x - x/2 - 3x/8 = 9

⇒ (8x-4x-3x)/8 = 9

⇒ x/8 = 9

⇒ x = 9×8 = 72

Hence, the total number of deer in the herd is 72.

Answer 2

Given :

• Half of a herd of deer are grazing in the field.
• Three fourth of the remaining herd are playing nearby.
• Rest 9 deers are drinking water from the pond.

To Find :

• The number of deer in the herd = ?

Solution :

Let,

• the number of deer in the herd be x.

Case 1 :

• Half of the deer are grazing in the field.

$\sf : \implies{Number\:of\:deer\:grazing\:in\:field\:=\:\dfrac{x}{2}}\:\:\:\:$

Case 2 :

• The remaining ¾ of deer are playing nearby.

$\sf : \implies{Remaining\:deer\:=\:\dfrac{3}{4}\:\times\:\big(x-\dfrac{x}{2}\big)}$

$:\implies\sf{\dfrac{3}{4}\:\times\:\big(\dfrac{2x-x}{2}\big)}$

$:\implies \sf{\dfrac{3}{4}\:\times\:\dfrac{x}{2}}$

$:\implies \sf{\dfrac{3x}{2\:\times\:4}}$

$:\implies \sf{\dfrac{3x}{8}\:\:\:\:(ii)}$

(iii)Case 3 :

• The number of deer drinking water in the pond is 9.

Equation :

• The total number of deer will be sum of (i), (ii) and the deer drinking water in the pond.

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

$:\implies \sf{\dfrac{8x+6x}{16}+9\:=\:x}$

$:\implies \sf{\dfrac{14x}{16}+9=x}$

$:\implies \sf{\dfrac{14x+144}{16}=x}$

$\sf:\implies {14x+144=16x}$

$:\implies \sf{14x-16x=-144}$

$:\implies \sf{\cancel{-}2x=\:\cancel{-}144}$

$:\implies \sf{x=\dfrac{-144}{-2}}$

$:\implies \sf{x=72}$

number of deer in the herd = 72