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?

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x3wolfygri · Accepted Answer

We can create a system of equations to address the issue because we are aware that chickens and rabbits both have one head, two legs, and four legs, respectively.Assume that r is the number of rabbits and that c is the number of chickens.The equation can be expressed in word form as follows for heads:(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:      1    c    +    1    r    =    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:      2    c    +    4    r    =    200  So now we have our system of equations:      c    +    r    =    72        2    c    +    4    r    =    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    +    2    r    =    100  We can now subtract the first equation from the second equation because the coefficient of c in both equations is now equal to 1:      c    +    2    r    -          (      c      +      r      )        =    100    -    72        c    +    2    r    -    c    -    r    =    28   by the distributive propertyBy 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.

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?

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