Let the number of deer be x.
Number of deer grazing in the field = x/2
Number of deer playing nearby = 3/4 x Number of remaining deer
= 3/4 x (x - x/2) = 3/4 x x/2 = 3x/8
Number of deer drinking water from the pond = 9
x - (x/2 + 3x/8) = 9
x - (4x + 3x/8) = 9
x - 7x/8 = 9
x/8 = 9
Multiplying both sides by 8, we obtain
x = 72
Hence, the total number of deer in the herd is 72..