Question

Each sheep has 4 legs and each chicken has 2 legs. If I count 50 heads and 140 feet total, how many sheep are there?​

Answer 1

`20\:\mathrm{sheep}`

Explanation:

We can write the following system of equations:

`\begin{cases}2c+4s=140,\\c+s=50\end{cases}`, where
`c` is the number of chickens and
`s` is the number of sheep.

Multiply the second equation by
`-2` and add both equations to solve for
`s`:

`\begin{cases}2c+4s=140,\\-2c-2s=-100 \end{cases},\\2s=40,\\s=\fbox{$20$}`.