Question

There are $1000$ rabbits and chickens on a farm and together they have $3150$ legs.

How many rabbits and how many chickens are there on the farm?

Answer 1

Step-1: Given and assume:

Total number of animals $=1000$(rabbits and chickens)

Total number of legs $=3150$

Let,

Rabbit denoted by $\mathrm{R}$.

chicken denoted by $\mathrm{C}$.

$\mathrm{R}+\mathrm{C}=1000...\left(\mathrm{i}\right)$

Since we know a rabbit has $4$ legs and a chicken has $2$ legs, then the equation is calculated.

$4\mathrm{R}+2\mathrm{C}=3150...\left(\mathrm{ii}\right)$

Step-2: To find

We have to determine the number of rabbits and chickens on the farm.

Step-3: Calculation

By multiplying the value $4$ in the equation $\left(\mathrm{i}\right)$and subtracting from the equation $\left(\mathrm{ii}\right)$, we get

$$\begin{gathered} \mathrm{R}+\mathrm{C}=1000...\left(\mathrm{i}\right)\times 4 \\ 4\mathrm{R}+2\mathrm{C}=3150...\left(\mathrm{ii}\right) \end{gathered}$$

$\begin{array}{rcl}4\mathrm{R}+4\mathrm{C}& =& 4000\\ 4\mathrm{R}+2\mathrm{C}& =& 3150\\ --& =& -\\ & \Rightarrow & 2\mathrm{C}=850\\ & \Rightarrow & \mathrm{C}=\frac{850}{2}\\ & \Rightarrow & \mathrm{C}=425\end{array}$

We are putting the $C$ value into the equation $\left(\mathrm{ii}\right)$.

$\begin{array}{rcl}4\mathrm{R}+2\left(425\right)& =& 3150\\ & \Rightarrow & 4\mathrm{R}+850=3150\\ & \Rightarrow & 4\mathrm{R}=3150-850\\ & \Rightarrow & 4\mathrm{R}=2300\\ & \Rightarrow & \mathrm{R}=\frac{2300}{4}\\ & \Rightarrow & \mathrm{R}=575\end{array}$

Hence, the number of rabbits and chickens on the farm is “$\mathbf{575}$ and $\mathbf{425}$”.