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?

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

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