An algebra teacher drove by a farmyard full of chickens and pigs. the teacher happened to notice that there were a total of 100 heads and 270 legs. how many chickens were there? how many pigs were there? (must show work)

Both pigs and chickens have one head :P So:

100=p+c  let's solve this for c:

c=100-p  we will need this value of c in a moment.

Chickens have 2 legs while pigs have 4 and we are told that there are 270 legs:

2c+4p=270, now using the value of c we found earlier in this we get:

2(100-p)+4p=270

200-2p+4p=270

2p+200=270

2p=70

p=35, and since c=100-p

c=65

So there were 35 pigs and 65 chickens.