farm mathcoolhistory

June 30, 2008

So back in high school my calc teacher (Mr. Pawlowski! Yay old yearbooks.) gave me an interesting way of solving this one classic-sounding algebra problem.

Like many math problems, the premise is a bit absurd: Farmer Brown knows he has, I dunno, 30 animals, cows and chickens. He doesn't know how many of each he has, but he does know that among them they have, say, 74 legs. (Why Farmer Brown is able to count legs but not animals, and not distinguish a chicken leg from a cow egg, is not made clear...)

Now there's the fancy-pants school-larnin' way of solving this: (let c be the number of chickens, m (for moo) the number of cows)
we know c+m=30
thus c = 30 - m
plus the legs means (c*2)+(m*4)=74
((30-m)*2)+4m=74
60-2m+4m=74
60+2m=74
30+m=37
m=7
and c = 23
 Cosmic Cow Says: "Hey, speaking of cows standing, anyone remember the show Too Close for Comfort?" "Monroe said his secret was being able to draw an inoffensive udder!"
but Farmer Brown doesn't know from Algebra. So what does he do? He has all the cows stand up on their hind legs! (and part of the fun of this is the teacher demonstrating what a cow on two legs looks like.) Since he knows he has 30 animals, he can know without counting that there are 60 legs on the ground. 14 legs unaccounted for, 2 each per cow, so there must be 7 cows, and 30-7=23 chickens.

That math seems a lot easier to do in your head! I'm not sure what the equations for it look like though... let me see...
c + m = 30
he quickly figured 2 * (c + m) = 60
but he knows 2c + 4m = 74 I guess he was able to tell that
(2c + 4m) - (2c + 2m) = 74 - 60
2m = 14
m = 7
c = 23
So that's a lot of steps that seemed easier to manage when you chunked things the right way. Maybe it's more like
Let a be the number of animals
t be the total number legs (2c + 4m), 74
let d be the number of legs down, 2*a, 60
d - t = 14
2m = 14 (I think that's the smart bit)
m = 7
c = a - m = 23
I'm not quite sure what the takeaway math lesson from this is... maybe it's the use of more variables when you're trying to do stuff in your head?

Why are the Onion headlines on the Slate sidebar all about homosexuality? Celebration of the CA ruling or what?