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September 14th, 2018, 06:44 AM   #1
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Number of sheeps

A farmer rears sheep and chickens at his farm. The number of sheep is 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 sheeps = S Number of Chickens = C

We know that there is one third of sheeps than chickens. so, (1/3)S = C

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

I got stuck here and couldn't get the correct answer.
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September 14th, 2018, 07:07 AM   #2
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Quote:
The number of sheep is 1/3 the number of chickens.
$\displaystyle S = \frac{C}{3} \implies C = 3S$

Quote:
There are 96 fewer sheep legs than chicken legs.
$\displaystyle 4S = 2C + 96$


substitute $3S$ for $C$ in the last equation ...

$\displaystyle 4S = 2(3S) + 96$

solve for $S$
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September 14th, 2018, 02:27 PM   #3
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Quote:
Originally Posted by skeeter View Post
$\displaystyle S = \frac{C}{3} \implies C = 3S$
I see where I made the mistake. One third of the total chicken.

Quote:
Originally Posted by skeeter View Post

4S=2C+96

substitute 3S for C in the last equation ...

4S=2(3S)+96
-2S = 96. I'm not sure about this.

Thank you.

Last edited by xoritos; September 14th, 2018 at 03:26 PM.
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September 14th, 2018, 05:20 PM   #4
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C = 3S [1]

2C - 4S = 96 [2]

Substitute [1] in [2]:
2(3S) - 4S = 96
6S - 4S = 96
2S = 96
S = 48 : C = 3S = 144

I think Skeeter made a typo...

...hmmm, think I'll have a snack of chicken legs
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Last edited by Denis; September 14th, 2018 at 05:23 PM.
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September 15th, 2018, 01:49 AM   #5
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As each sheep's 4 legs are 2 fewer than 3 chickens' 6 legs, number of sheep = 96/2 = 48.
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September 15th, 2018, 06:05 AM   #6
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Thank you.
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