Question

there are multiple chickens and rabbits in a cage there are 72 heads and 200 feet inside of the cage how many chickens are in there and how many rabbits

Answer 1

The answer is 44 chickens and 28 rabbits.

We have a system of two equations.
x - the number of rabbits
y - the number of chickens

Both chicken and rabbit have only 1 head, so the first equation is: x + y = 72.
Since rabbits have 4 legs and chickens 2 legs, the second equation is: 4x + 2y = 200.

Now, let's solve the system:
x + y = 72
4x + 2y = 200
___________
y = 72 - x
⇒ 4x + 2 · (72 - x) = 200
4x + 2 · 72 - 2 · x = 200
4x + 144 - 2x = 200
2x + 144 = 200
2x = 200 - 144
2x = 56
⇒ x = 56 ÷ 2 = 28
So, there are 28 rabbits.

Since
y = 72 - x = 72 - 28 = 44,
there are 44 chickens.