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..