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.

AcademicMathematicsNCERTClass 8

Given:

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. 

To do:

We have to find the number of deer in the herd.

Solution:

Let the total number of deer be $x$
This implies,

Number of deer grazing in the field $=$ Half of the herd

$=\frac{x}{2}$

Number of deer playing $=\frac{3}{4}(x-\frac{x}{2})$

$=\frac{3}{4}(\frac{x}{2})$

$=\frac{3x}{8}$

Number of deer drinking water from the pond $=9$

Therefore,

$x=\frac{x}{2}+\frac{3x}{8}+9$

$x-\frac{x}{2}-\frac{3x}{8}=9$

$\frac{8(x)-4(x)-3x}{8}=9$

$8x-4x-3x=8(9)$

$8x-7x=72$

$x=72$

The total number of deer in the herd is $72$. 

raja
Updated on 10-Oct-2022 13:47:38

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