In a pen with rabbits and chickens someone counted 25 heads and 80 legs a rabbit has four legs and each chicken has 2 legs, how many chickens and rabbits are there?

Let "rabbits" be represented by the variable "x"

and "chickens" be represented by the variable "y"

then in total we have 25 animals

so x + y = 25

-> y = - x + 25

and since a rabbit has four legs and a chicken has two legs

and there are 80 legs in total

4x + 2y = 80

-> 2x + y = 40

-> y = - 2x + 40

[I had solved for y for each equation]

and since we are looking for when y = y

-x + 25 = - 2x + 40 [we can solve for x from here]

x + 25 = 40 [added 2x to both sides]

x = 15 [subtracted 25 from both sides]

then we can plug this back into

y = - x + 25

to get y = - 15 + 25 = 10

therefore there are 15 Rabbits and 10 Chickens

I just kind of sat here playing with numbers i dont really know a shortcut but the answer is 10 chickens and 15 rabbits

10*2 = 20 each chicken has two legs so thats 10 heads 20 legs

15*4=60 each rabbit has four legs so thats 15 heads 60 legs

15+10=25 heads

20+60=60 legs