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 thenumber of deer in the herd.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{deer}\mathrm{in}\mathrm{the}\mathrm{herd}\mathrm{be}\mathrm{x}. \\ \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{deer}\mathrm{grazing}\mathrm{in}\mathrm{the}\mathrm{field}\mathrm{is}\left(\frac{1}{2}\right)\mathrm{x}. \\ \mathrm{Remaining}\mathrm{deer}=x-\frac{x}{2}=\frac{x}{2} \\ N\mathrm{umber}\mathrm{of}\mathrm{deer}\mathrm{playing}\mathrm{nearby}=\frac{3}{4}\left(\frac{x}{2}\right)=\frac{3}{8}x \\ \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{deer}\mathrm{drinking}\mathrm{water}\mathrm{from}\mathrm{the}\mathrm{pond}\mathrm{is}9. \\ \therefore 9+\frac{3}{8}x+\frac{1}{2}x=x \\ \Rightarrow \frac{72+3x+4x}{8}=x(\mathrm{multiplying}\mathrm{the}\mathrm{L}.\mathrm{H}.\mathrm{S}.\mathrm{by}8,\mathrm{which}\mathrm{is}\mathrm{the}\mathrm{L}.\mathrm{C}.\mathrm{M}.\mathrm{of}1,8\mathrm{and}2) \\ \Rightarrow 72+7x=8x(\mathrm{by}\mathrm{cross}\mathrm{multiplication})\Rightarrow 72=8x-7x\Rightarrow 72=x\Rightarrow x=72T\mathrm{otal}\mathrm{number}\mathrm{of}\mathrm{deer}\mathrm{in}\mathrm{the}\mathrm{herd}=72 \end{gathered}$$