My Math Forum Number of sheeps

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 September 14th, 2018, 05:44 AM #1 Member   Joined: Sep 2018 From: Japan Posts: 35 Thanks: 2 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.
September 14th, 2018, 06:07 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 $S$

September 14th, 2018, 01:27 PM   #3
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Quote:
 Originally Posted by skeeter $\displaystyle S = \frac{C}{3} \implies C = 3S$
I see where I made the mistake. One third of the total chicken.

Quote:
 Originally Posted by skeeter 4S=2C+96 substitute 3S for C in the last equation ... 4S=2(3S)+96

Thank you.

Last edited by xoritos; September 14th, 2018 at 02:26 PM.

 September 14th, 2018, 04:20 PM #4 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 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 Thanks from topsquark and xoritos Last edited by Denis; September 14th, 2018 at 04:23 PM.
 September 15th, 2018, 12:49 AM #5 Global Moderator   Joined: Dec 2006 Posts: 21,019 Thanks: 2254 As each sheep's 4 legs are 2 fewer than 3 chickens' 6 legs, number of sheep = 96/2 = 48. Thanks from xoritos
 September 15th, 2018, 05:05 AM #6 Member   Joined: Sep 2018 From: Japan Posts: 35 Thanks: 2 Thank you.

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