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 no. of deer in the herd. ​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large\underline{\green{\bf Given :-}}$

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• Half of a herd of deer are grazing in the field

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• Three fourths of the remaining are playing nearby

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• The rest 9 are drinking water from the pond

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$\large\underline{\red{\bf To \: Find :-}}$

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• Total number of deer

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$\large\underline{\orange{\bf Solution :-}}$

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• Let the total number of deer be "x"

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$\underline{\bold{\texttt{Deer grazing in field :}}}$

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Half of a herd of deer are grazing in the field

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➜ $\sf \dfrac { 1 } { 2 } × x$ ⚊⚊⚊⚊ ⓵

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$\underline{\bold{\texttt{Number of deer left now :}}}$

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➜ $\sf \dfrac { x } { 2 }$

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$\underline{\bold{\texttt{Number of deer playing nearby :}}}$

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Three fourths of the remaining are playing nearby

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$\sf \dfrac { 3 } { 4 } × \dfrac { x } { 2 }$

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➜ $\sf \dfrac { 3x } { 8 }$ ⚊⚊⚊⚊ ⓶

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$\underline{\bold{\texttt{Number of deer drinking water :}}}$

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➜ 9 ⚊⚊⚊⚊ ⓷

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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⟮ Equation ⓵ + ⓶ + ⓷ = Total number of deer ⟯

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

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➜ $\sf \dfrac { 4x + 3x + 72 } { 8 } = x$

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➜ $\sf \dfrac { 7x + 72 } { 8 } = x$

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➜ 7x + 72 = 8x

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➜ 8x - 7x = 72

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➨ x = 72

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• Hence there were total 72 deer in the herd

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