Question

There are multiple chickens and rabbits in a cage. There are 72 heads and 200 feet inside the cage. How many chickens are in there and how many rabbits?

Answer 1

represent
r=number of rabbits
c=number of chickens
1 rabbit=4 feet and 1 head
1 chicen=2 feet and 1 head

rabbits head+chicen heads=72
1r+1c=72
feet=200
4 times r+2 times c=200
4r+2c=200
divide both sides by 2
2r+c=100


we have
r+c=72
2r+c=100
make first equation negative and add to second equation

-r-c=-72
2r+c=100 +
1r+0c=28

r=28
subsitute
r+c=72
28+c=72
subtract 28
c=44

44 chickens and 28 rabits