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

Let the total number of deer in the herd be x.
According to question,
$x=\frac{x}{2}+\frac{3}{4}\times (x-\frac{x}{2})+9$
$\Rightarrow x-\frac{x}{2}=\frac{3x}{8}+9$
$\Rightarrow \frac{x}{2}-\frac{3x}{8}=9$
$\Rightarrow \frac{4x-3x}{8}=9\Rightarrow \frac{x}{8}=9$
$\Rightarrow x=9\times 8=72$

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