A farmer had sheep and hens in his barnyard....there where 40 heads
and 100 feet total including all sheep and hens.

How many hens and how many sheep did he have?

Hi jam369,

He would have had 30 hens and 10 sheep.

30x2=60  10x4=40  60+40=100 feet

30+10=40 heads

I hope that helps.

Best regards,
Rainbow

So as to (as the math teachers say) "show your work" a bit more, you could say:

Let X be the number of sheep.
Since you're told there are 40 heads, there are 40 animals. So if
there are X sheep, the number of hens is (40-X)

Sheep generally have 4 legs each; hens generally have 2.

So the number of sheep legs is 4X (four per sheep) and the number of
hen legs is 2(40-X) or (80-2X)

Since there are 100 legs total, that gives you the formula:

 4X + (80-2X) = 100

which solves down to:

X=10

So there are 10 sheep and 30 (i.e. 40-10) hens.

All assuming no mutant livestock with non-traditional numbers of heads
or feet, of course ;-)

Thanks for your help....I'm afraid I would be still be working on the problem.

jam369

The answer provided by Rainbow is entirely correct. Why this should
get four stars rather than five is a mystery. How could a 100% correct
answer be any better?

In this case the 4 stars is correct
- the right solution, but not the right answer

The methodology was missing (and that is what mattered)

  S + H = 40
  (S x 4) + (H x 2) = 100

=>  S = 40 - H
    (40 - H) * 4 + (H x 2 ) = 100     //  Substitution
    160 -4H + 2H = 100                //  Expand and use proper notation
    -2H = 100 - 160 = -60             //  Clarify
=>  H = 60 / 2 = 30                   //  Resolve 

    S + 30 = 40
=>  S = 40 - 30 = 10

Of course it is 'homework', but there is a strong possibility that the
parent is asking the question, most 10 year old kids don't have credit
cards.

Probably Rainbow had not figured that angle

Personally I reckon that Gurgle should allow an 'answer revision' feature
- otherwise the star ratings show 'right first time'
- which is largely a measure of the ability of the questioner to ask
for a clarification

In this case Jam369-ga  (March 1969 - aged 27 yrs) should have said :-
  'I see that but how do I explain it to my kid ?'

Of course, the correct question would be :-
  'I am tired, a hard day at the skunk works, and trying to explain
simultaneous equations to my (under!) 10 year old kid
- could you show the workings for ... '

I don't much like things going wrong
- with a few changes in the rules, this sort of thing would not happen again.

Hmm.. an ex-Camera Star Chamber might be an idea.