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# 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.

**Given:**

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.

**To do: **

We have to find the number of deer in the herd.

**Solution:**

Let the total number of deer be $x$

This implies,

Number of deer grazing in the field $=$ Half of the herd

$=\frac{x}{2}$

Number of deer playing $=\frac{3}{4}(x-\frac{x}{2})$

$=\frac{3}{4}(\frac{x}{2})$

$=\frac{3x}{8}$

Number of deer drinking water from the pond $=9$

Therefore,

$x=\frac{x}{2}+\frac{3x}{8}+9$

$x-\frac{x}{2}-\frac{3x}{8}=9$

$\frac{8(x)-4(x)-3x}{8}=9$

$8x-4x-3x=8(9)$

$8x-7x=72$

$x=72$

**The total number of deer in the herd is $72$. **

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