question_answer

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:

Let the total number of deer in the herd be x.

According to question,

\[\frac{x}{2}+\frac{3}{4}\left( x-\frac{x}{2} \right)+9=x\]

or,     \[\frac{x}{2}+\frac{3}{4}\times \frac{x}{2}+9=x\]

or,        \[\frac{x}{2}+\frac{3x}{8}+9=x\]

or,        7x + 72 = 8x

or,       \[7x-8x=-72\]

or,        \[-x\text{ }=-72\,\,\,or,\,\,x\text{ }=\text{ }72\]

Hence, the required number of deers in the herd are 72.