8.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.

Let the number of deer = x.
As per the condition given, we have

\(\frac { x }{ 2 }\) deer are grazing in the field.

Remaining deers=\(x-\frac{x}2=\frac{x}2\)

∴ we have \(\frac{x}2×\frac{3}4=\frac{3x}8 \) deers playing near by.

Number of the deers drinking water=9

∴ we have, \(\frac{x}2+\frac{4x}2+9=x\)

\(\Rightarrow 8×\frac{x}2+8×\frac{3x}8+8×9=8×x\)

\(\Rightarrow 4x+3x+72=8x\)

\(\Rightarrow 7x-8x=-72\)

\(\Rightarrow -x=-72\)

\(\Rightarrow x=72\)

Hence the number of deer in the herd is 72.