Question

Half of a herd of deer are grazing in the field and $ \dfrac{3}{4}th $ of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find the total number of deer in the herd.

Answer 1

Hint: You can see that the question is based on basic algebra. You have to find the total number of deer in the herd. For that we will find the number of deer separately, who are grazing in the field or who are playing in the field and also who are drinking water from the pond. We will add them and we will get the total number of deer in the herd.

Complete step-by-step answer:
It is mentioned in the question that the half number of deer of the given hard are grazing in the field.
And, from the remaining half number of deer in the herd $ \dfrac{3}{4}th $ of it are playing nearby.
And the rest of the 9 deer are drinking water from the pond.
We need to find the total number of deer in the herd.
We can write the total number of the deer as,
Total no. of deer = No. of deer grazing + No. of deer playing + No. of deer drinking water …. (1)
Firstly, we will find the number of their grazing in the ground.
Let us suppose, the total number of deer in the herd be x
Now, as it is mentioned half of the deer in the herd are grazing in the field so, the number of halves of the deer in the herd is given by $ \dfrac{x}{2} $
Hence, the number of deer are grazing in the field is $ \dfrac{x}{2} $
Secondly, we need to find out the number of deer who are playing.
We knew that, $ \dfrac{3}{4}th $ of the remaining half (other than the half who are grazing in the field) deer of the herd are playing.
The number of deer in the remaining half is $ x - \dfrac{x}{2} = \dfrac{x}{2} $
From, the remaining half $ \dfrac{x}{2} $ deer in the herd, $ \dfrac{3}{4}th $ of them are grazing, which is given by
 $ \dfrac{3}{4}\,of\,\dfrac{x}{2} = \dfrac{3}{4} \times \dfrac{x}{2} $ , we can write it as \[\dfrac{{3x}}{8}\]
Hence, the number of deer playing is \[\dfrac{{3x}}{8}\]
Also, the rest at 9 dears are drinking water from the pond which means,
The number of deer drinking water from the pond= 9
Now, if we put a number of deer in the equation (1), we obtain,
 $
\Rightarrow x = \dfrac{x}{2} + \dfrac{{3x}}{8} + 9 \\
\Rightarrow x - \left( {\dfrac{x}{2} + \dfrac{{3x}}{8}} \right) = 9 \\
\Rightarrow x - \dfrac{{7x}}{8} = 9 \\
\Rightarrow 8x - 7x = 72 \\
  \Rightarrow x = 72 \\
 $
Hence, the total number of deer in the field is 72

Note: Students often confuse what to consider x. Always remember you should consider the parameter as x that is asked to you to find out. As for example you are told to find out the total number of deer in the question, you consider it as x. Try to avoid arithmetic mistakes.