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

Find the total number of deer

Let the total number of deer be $x$

Number of deer grazing in the field$=\frac{1}{2}x$

Number of deer playing in the field$=\frac{3}{4}\times \frac{1}{2}x$

Number of deer drinking water from the pond is

$$\begin{gathered} \Rightarrow 9=x-\frac{1}{2}x-\frac{3}{8}x \\ \Rightarrow 9=\frac{8x-4x-3x}{8} \\ \Rightarrow 9=\frac{1}{8}x \\ \Rightarrow 72=x \end{gathered}$$

Hence, the total number of deer in the herd are $72$.