Question

Half of a herd of deer are grazing in the field and three fourth of remaining are playing nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.

Answer 1

Hint: First we will assume that the number of deers in the herd will be \[x\] and then find the half of the herd grazing in the field by dividing the number of deers in the herd be \[x\] by 2. Then we will find the remaining of the herd by subtracting half of the herd from the number of deers and take the \[\dfrac{3}{4}\]th of the remaining half are playing and take the obtained value equal to 9 to find the required value.

Complete step-by-step answer:
We are given that half of a herd of deer are grazing in the field and three fourth of remaining are playing nearby.
Let us assume that the number of deers in the herd be \[x\].
We will now find the half of the herd grazing in field by dividing the number of deers in the herd be \[x\] by 2, we get
\[ \Rightarrow \dfrac{x}{2}\]
Then finding the remaining of the herd by subtracting half of the herd from the number of deers, we get
\[
   \Rightarrow x - \dfrac{x}{2} \\
   \Rightarrow \dfrac{x}{2} \\
 \]
Taking the \[\dfrac{3}{4}\]th of the remaining half are playing, we get
\[
   \Rightarrow \dfrac{3}{4} \times \dfrac{x}{2} \\
   \Rightarrow \dfrac{{3x}}{8} \\
 \]
Then finding the remaining of the deers drinking water by subtracting half of the herd playing from the remaining of deers, we get
\[
   \Rightarrow \dfrac{x}{2} - \dfrac{{3x}}{8} \\
   \Rightarrow \dfrac{{4x - 3x}}{8} \\
   \Rightarrow \dfrac{x}{8} \\
 \]
We are given that the remaining deers drinking water is 9, so we have
\[ \Rightarrow \dfrac{x}{8} = 9\]
Multiplying the above equation by 8 on both sides, we get
\[
   \Rightarrow 8 \times \dfrac{x}{8} = 9 \times 8 \\
   \Rightarrow x = 72 \\
 \]
Therefore, the total number of deers in the herd is 72.

Note: In solving these types of questions, students need to read the question properly before writing. Students have assumed the number of deers with some variable to find the required value. The possibility of error in this question can be trying to find the value of \[x\] by not taking it equal to 9, which is wrong. Also, avoid calculation mistakes.