Question

There are multiple chickens and rabbits in a cage. There are 72 heads and 200 feet inside of the cage. How many chickens and rabbits are in there?

Answer 1

Hint: In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value. Here we are given two variables i.e. chickens and rabbits in the cage. Also given that, there are 72 heads and 200 feet in the cage. From this information we will get two equations. Solving them, we will get the final output.

Complete step by step answer:
Given that, there are 2 different animals and they are chickens and rabbits.
Also given that there are 72 heads and 200 feet in all inside the cage.
Since we know that, each rabbit (r) and chicken (c) have one head.
From the given information, we get the equation (i) as:
\[r + c = 72\]
Also, we know that a rabbit has 4 feet and a chicken has 2 feet.
From this, we get the new equation (ii) as:
\[4r + 2c = 200\]

We will solve the given equations as below:
First we will multiply the given equation by 2 and we will get,
\[2r + 2c = 144\] ---- (iii)
Next, we will subtract (iii) from (ii), we will get,
\[ \Rightarrow 4r - 2r = 200 - 144\]
\[ \Rightarrow 2r = 56\]
\[ \Rightarrow r = 28\]
Now, substitute this value of r in equation (i), we will get,
\[ \Rightarrow 28 + c = 144\]
\[ \Rightarrow c = 144 - 28\]
\[ \Rightarrow c = 44\]
Thus, we have 44 chickens (4) and 28 rabbits (r).

Hence, there are 44 chickens and 28 rabbits in the cage.

Note: Linear equations are also first-degree equations as they have the highest exponent of variables as one. An equation for a straight line is called a linear equation. The process of finding the value of the variable is called solving the equation.