Quiz question No 3 (medium)

[Doctor]

Evening,

One day, a punter went to the horse racing, Instead of counting the numbers of humans and horses, he instead counted 74 heads and 196 legs. Yet he knew the number of humans and horses there. How did he do it, and how many humans and horses are there?


Need to know your maths for this one.

Regards
Bloggy

 

[LuptonM]

So easy!!!!!!!

let l=legs
h=heads]

n= no of horses
m= no of humans

humans: 2l+1h
horses: 4l+1h

n(4l+1h) +m(2l+h) = 74h + 196l

4n+2m=196

n+m=74

m=74-n

thus 4n +2(74-n)=196

2n=48

no of horses is thus 24

no of humans is 74-24= 50

 

[Gary]

I agree with Lupton

let number of human=x & horse=y
since human & horse have one head each then,
x+y=74.....(1)
=>x=74-y
and human have 2 legs & horses have 4 legs then
2x+4y=196 .....(2)
=>2(74-y) +4y=196
=>148 -2y+4y=196
=>2y=196-148
=>2y=48
=>y=48/2
=>y=24
Now, from (1)
x+24=74
=>x=74-24
=>x=50
The numbers of human=50
& horses=24

 

[Alf]

Ooo, I feel like Carol Vordermann - I did it a different way, without the alphabet.

196 divided by 2 gives 98 pairs of legs (Both horse and humans have at least a pair of legs - assuming there were no amputees)
98 - 74 heads leaves 24 pairs "spare"
Ergo 24 horses
74 total heads - 24 horses heads* = 50 human heads
Thus 50 humans and 24 horses.

I'm sure that would have got me a "tut-tut" from my old maths teacher as methods go, but it worked for me.

*Available for any American Italian business dealings...

 

[Steve Maskery]

Ooo, I feel like Carol Vordermann

So do I......


S
Well someone had to post it.

 

[cambournepete]

I did it Gary's way, but I really like Alf's lateral thinking

 

[JonnyD]

I just typed 74 legs 196 heads into google http://answers.yahoo.com/question/index ... 909AAn5jht

saved a lot of working out

cheers

jon

 

[PeterBassett]

I agree with Lupton

let number of human=x & horse=y
since human & horse have one head each then,
x+y=74.....(1)
=>x=74-y
and human have 2 legs & horses have 4 legs then
2x+4y=196 .....(2)
=>2(74-y) +4y=196
=>148 -2y+4y=196
=>2y=196-148
=>2y=48
=>y=48/2
=>y=24
Now, from (1)
x+24=74
=>x=74-24
=>x=50
The numbers of human=50
& horses=24

Copy paste bull dung from
http://answers.yahoo.com/question/index ... 909AAn5jht

Get the dunce cap!

Well done to those who worked it out.

 

[jeffinfrance]

alf, that's genius. :mrgreen:

unfortunately i'd just had a big spliff before reading last night. put the kybosh on my algerba skills.

should have had another, might have spotted your out of the box version.

jeff