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

44 chicken and 28 rabbits

Given:
chicken head + rabbit head = 72 heads
chicken feet + rabbit feet = 200 feet

c + r = 72
2c + 4r = 200

find the value of c using the 1st equation:
c = 72 - r

substitute c by its value in the 2nd equation:
2c + 4r = 200
2(72-r) + 4r = 200
144 - 2r + 4r = 200
2r = 200 - 144
2r = 56
r = 56/2
r = 28

c = 72 - r
c = 72 - 28
c = 44

c = 44 ; r = 28

To check:
2c + 4r = 200
2(44) + 4(28) = 200
88 + 112 = 200
200 = 200