Question

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

Answer 1

There are 44 chickens and 28 rabbits in the cage.

Explanation:

Since we know that both chickens and rabbits only have `1` head each and chickens have `2` legs and rabbits have `4` legs, we can set up a system of equations to solve the problem.

Let `c` be the number of chickens and `r` be the number of rabbits.
For heads, we can write the equation out in word form as:
(number of heads per chicken)(number of chickens) + (number of heads per rabbit)(number of rabbits) = (total number of heads)
In algebraic form, this equation would look like this:
`1c+1r=72` or `c+r=72`

Similarly for legs, we can write the equation out in word form as:
(number of legs per chicken)(number of chickens) + (number of legs per rabbit)(number of rabbits) = (total number of rabbits)
In algebraic form, this equation would look like this:
`2c+4r=200`

So now we have our system of equations:
`c+r=72`
`2c+4r=200`

Now we can use elimination (or substitution) to solve for c and r:
The second equation can be reduced by dividing both sides by 2:
`c+2r=100`

Here since both equations now have the coefficient of `c` as 1, we can subtract the first equation from the second equation:
`c+2r-(c+r)=100-72`
`c+2r-c-r=28` by the distributive property
By simplifying and combining like-terms, we get:
`r=28`

Now we can substitute this value of r into the first equation, `c+r=72`:
`c+28=72`
`c+28-28=72-28`
`c=44`

Therefore, there are 44 chickens and 28 rabbits in the cage.