A farmer raises sheep and chickens at his farm. The number of sheep is $\frac{1}{3}$ the number of chickens. There are $96$ fewer sheep legs than chicken legs. How many sheep are there at the farm?

My work:

Number of sheep = $S$

Number of Chickens = $C$

We know that there is one third of sheep than chickens. so, $\frac{1}{3}S = C$

We know that there are 96 fewer sheep legs than chicken leg. so, $2C = 4S - 96$

I got stuck here.

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RukaiPlusPlus is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
up vote 1 down vote accepted

You need to change your first equation. If the number of sheep is $\frac{1}{3}$ the number of chicken then $3S = C$.

Also in your second equation, the $-$ needs to be a $+$ because if there are fewer sheep legs than chickens then you'll need to add 96 on the sheep value.

Then combine the equations and you'll get the answer.

  • Okay, after some time, I finally understand why you had to add the 96. Thank you. – RukaiPlusPlus Sep 15 at 22:42

The number of sheep $S$ is $\frac{1}{3}$ the number of chickens $C$ so $S =\frac{1}{3}C $ and also $4S=2C - 96$ $$\begin{cases} S=\frac{1}{3}C \\ 4S=2C - 96 \end{cases} \Leftrightarrow \begin{cases} C=3S \\ 4S=6S - 96 \end{cases} \Leftrightarrow \begin{cases} C=3S \\ 2S= 96 \end{cases} \Leftrightarrow \begin{cases} C=3S \\ S= 48 \end{cases} \Leftrightarrow \begin{cases} C=144 \\ S= 48 \end{cases}$$

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PrinceOfBorgo is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
  • $$2c=4s+96 $$ look at your 2nd equation – Deepesh Meena Sep 14 at 13:57
  • Oh sure! I copied the same equations of the post and only corrected one, thanks! – PrinceOfBorgo Sep 14 at 13:57

We know that there is one-third of sheep than chickens. so, $S=\frac{1}{3}C$

We know that there are 96 fewer sheep legs than the chicken leg. so,$ 2C-96=4S$

$$C=3S$$ $$2C-96=4S$$

Two equations two variables can you solve from here?

  • I'm not understanding why it's 2C - 96 = 4S? I would expect 2C+96 = 4S – RukaiPlusPlus Sep 14 at 22:21
  • there are 96 fewer sheep legs than the chicken legs. which means that sheep's legs are 96 less than that of cats cat has 2c legs sheep has 4S legs – Deepesh Meena Sep 14 at 22:22
  • I'm guessing the "than" makes the difference? so it means chicken legs is 96 less than sheep legs? Because I read it as sheep legs is 96 less than chicken legs. – RukaiPlusPlus Sep 14 at 22:38

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