Half of a herd of deer are grazing in the field and three fourth of the remaining are playing nearby.The rest 9 are drinking water from the pond.Find the number of deer in the herd.
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Step-by-step explanation:
Let the total number of deer in the herd be x.
According to question, x=\frac{x}{2}+\frac{3}{4}\times\left(x-\frac{x}{2}\right)+9x=
2
x
+
4
3
×(x−
2
x
)+9
\Rightarrow x=\frac{x}{2}+\frac{3}{4}\left(\frac{2x-x}{2}\right)+9⇒x=
2
x
+
4
3
(
2
2x−x
)+9
\Rightarrow x=\frac{x}{2}+\frac{3}{4}\times\frac{x}{2}+9⇒x=
2
x
+
4
3
×
2
x
+9
\Rightarrow x=\frac{x}{2}+\frac{3}{8}x+9⇒x=
2
x
+
8
3
x+9
\Rightarrow x-\frac{x}{2}-\frac{3x}{8}=9⇒x−
2
x
−
8
3x
=9
\Rightarrow\frac{8x-4x-3x}{8}=9⇒
8
8x−4x−3x
=9
\Rightarrow\ \frac{x}{8}=9⇒
8
x
=9
\Rightarrow x=9\times8=72⇒x=9×8=72
Hence, the total number of deer in the herd is 72.
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