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 be x.
Number of deer grazing in the field = `x/2`
Number of deer playing nearby = `3/4 xx "Number of remaining deer"`
`= 3/4 xx (x - x/2) = 3/4 xx 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.