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.
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 $72$.
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