Can Anyone Show How To Work Out Mindbender Question1 Please ?

[treese]

Auntie Birdie had a farm which had only chickens and cows. Birdie counted 55 heads and 156 feet in the farmyard including her own. How many cows did she have on her farm?

[fiction-factory]

k chickens and w cows
k + w = 55
so 2k +2w =110
we also know 2k +4 w = 156

So 2w= 46
so w=23
so k =32

[fiction-factory]

So 32 chickens and 23 cows

[mallyh]

i don't follow how you did it fiction but well done xx

[weecalf]

What about dear old aunties head?

[Togo]

surely its 31 chickens . auntie birdie had 1 head and 2 feet. she counted her own

[fiction-factory]

Well spotted- I didn't see that bit weecalf. Just tweak it then treese

[Calibax]

You fell into the same trap as I did FF. 55 heads and 156 feet
INCLUDING HER OWN.

[Cloverjo]

F-f, you didn't include the woman, so 31 chickens.

[Cloverjo]

Oops, I'm too late as usual.

[fiction-factory]

She clearly counts her own feet (assuming she's a biped) but can she see her own head to count it?

[fiction-factory]

Anyway it's still 23 for cows is it

[Prudie]

Well I've spent a while typing this in Word so whether it's wrong or right I'm posting it anyway:

You have to use algebra:
Let the number of cows be X
Let the number of chicken be Y

Each cow has 1 head and 4 feet
Each chicken has 1 head and 2 feet
The farmer has 1 head and 2 feet

So the total number of heads is X + Y +1
The total number of feet is 4X + 2Y + 2

So we know X+Y + 1 = 55 (all the heads) and 4X +2Y + 2 is 156 (all the feet)

Simplify that to 2 simultaneous equations:
X+Y = 54
4X + 2Y = 154

Double the top one : 2X+2Y = 108 and then take away from the 2nd to give

2X = 46

So there are 23 cows

[weecalf]

Do cows not have hoofs and its birdie I'm now seeing

[treese]

Thanks to all who have helped with this one, love the responses, but still trying to understand as I'm fairly new to this type of question.

[fiction-factory]

One way is to make a guess. Knowing there are 55 heads you could start off with 27 chickens, 27 cows and Auntie Bertie. Work out whether you are too high or too low for the number of feet. If you are too high then reduce the number of cows slightly and increase the number of chickens accordingly. You'll soon get to the answer

[sandyRoe]

if they were all chickens there'd be 110 legs(including auntie) The fact that there's 46 legs too many for that means 23 must be cows.