Answer

Verified

389.7k+ views

**Hint:**Here we need to find the number of deer and human visitors in the park. For that, we will first assume the number of legs of human visitors and number of legs of deer to be any variable. Then we will add both of them and then we will equate the sum with the given number of legs. From there, we will get the first equation including all the variables. Then we will form the second equation using the information given in the question. We will solve these two equations to get the values of the number of humans and deer in the park.

**Complete step by step solution:**

Let the total number of legs of deer be \[x\] and let the total number of legs of human visitors be \[y\].

It is given that the sum of the number of legs of deer and human visitors is 132. Therefore,

\[x + y = 132\] ……… \[\left( 1 \right)\]

We know that 1 deer has 4 legs and 1 head and 1 human visitor has 2 legs and 1 head. So,

Number of heads of deer \[ = \dfrac{x}{4}\]

Number of heads of human visitors \[ = \dfrac{y}{2}\]

It is given that the sum of the number of heads of deer and human visitors is 39.

\[ \Rightarrow \dfrac{x}{4} + \dfrac{y}{2} = 39\] …….. \[\left( 2 \right)\]

Now, we will multiply 4 on both sides of equation \[\left( 2 \right)\].

\[ \Rightarrow x + 2y = 39 \times 4\]

On multiplying the terms, we get

\[ \Rightarrow x + 2y = 156\] …………. \[\left( 3 \right)\]

On subtracting equation \[\left( 1 \right)\] from equation \[\left( 3 \right)\], we get

\[\begin{array}{l}x + 2y - \left( {x + y} \right) = 156 - 132\\ \Rightarrow x + 2y - x - y = 24\end{array}\]

Adding and subtracting like terms, we get

\[ \Rightarrow y = 24\]

Now, we will substitute the value of \[y\] in equation \[\left( 1 \right)\].

\[x + 24 = 132\]

Now, we will subtract 24 from both sides. Therefore, we get

\[\begin{array}{l} \Rightarrow x + 24 - 24 = 132 - 24\\ \Rightarrow x = 108\end{array}\]

Now, substituting the value of \[x\] and \[y\] the equation of number of heads of deer and humans, we get

Number of heads of deer \[ = \dfrac{x}{4} = \dfrac{{108}}{4} = 27\]

Number of heads of human visitors \[ = \dfrac{y}{2} = \dfrac{{24}}{2} = 12\]

**Hence, the number of deer and human visitors in the park are 27 and 12 respectively.**

**Note:**

Here, we have framed two linear equations in two variables based on the given information. Linear equations are the equations that have the highest degree of the variable as 2. Linear equation in two variables means there are two distinct variables and both have the highest degree 1. We have solved the two linear equations to find the value of the two variables.

Recently Updated Pages

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

10 examples of friction in our daily life

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Who was the first to raise the slogan Inquilab Zindabad class 8 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

One cusec is equal to how many liters class 8 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

A resolution declaring Purna Swaraj was passed in the class 8 social science CBSE