Three –fourths of a herd of deer are grazing in the field and half of the remaining are playing nearby. The rest 9 are drinking water from the field .Find the number of deer in the herd.
Answers
Q8) 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.
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Solution:
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)+9
\Rightarrow x=\frac{x}{2}+\frac{3}{4}\left(\frac{2x-x}{2}\right)+9
\Rightarrow x=\frac{x}{2}+\frac{3}{4}\times\frac{x}{2}+9
\Rightarrow x=\frac{x}{2}+\frac{3}{8}x+9
\Rightarrow x-\frac{x}{2}-\frac{3x}{8}=9
\Rightarrow\frac{8x-4x-3x}{8}=9
\Rightarrow\ \frac{x}{8}=9
\Rightarrow x=9\times8=72
Hence, the total number of deer in the herd is 72.
Answer:
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)+9
\Rightarrow x=\frac{x}{2}+\frac{3}{4}\left(\frac{2x-x}{2}\right)+9
\Rightarrow x=\frac{x}{2}+\frac{3}{4}\times\frac{x}{2}+9
\Rightarrow x=\frac{x}{2}+\frac{3}{8}x+9
\Rightarrow x-\frac{x}{2}-\frac{3x}{8}=9
\Rightarrow\frac{8x-4x-3x}{8}=9
\Rightarrow\ \frac{x}{8}=9
\Rightarrow x=9\times8=72
Hence, the total number of deer in the herd is 72.