Answer:
Let the number of deer in the herd be \[x\]. Then, number of deer grazing in the field \[=\frac{x}{2}\] \[\therefore \] Number of remaining deer \[=x-\frac{x}{2}=\frac{x}{2}\] \[\therefore \] Number of deer playing nearby \[=\frac{3(x/2)}{4}=\frac{3x}{8}\] Number of deer drinking water from the pond \[=x-\left( \frac{x}{2}+\frac{3x}{8} \right)\] \[=x-\left( \frac{4x+3x}{8} \right)\] \[=x-\frac{7x}{8}\] \[=\frac{8x-7x}{8}=\frac{x}{8}\] According to the question, \[\frac{x}{8}=9\] \[\Rightarrow \] \[x=9\times 8=72\] | Multiplying both sides by 8 Hence, the number of deer in the herd is 72. 79 Check: \[\frac{72}{2}=36,\] \[\frac{3}{4}(36)=27\] \[72-(36+27)\,=72-63=9\] Hence, the result is verified.
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