A building holds chickens and mice. Jen counted 60 feet and 23 heads. How many of each animal are there?

Please answer and explain this to me. By the way...mice have 4 feet and chickens have 2, in case you forgot.A building holds chickens and mice. Jen counted 60 feet and 23 heads. How many of each animal are there?
C=number of chickens


M=number of mice





So you get the simultaneous equations





2C+4M=60


C+M=23


Rearrange


C=23-M


Substitute


2(23-M)+4M=60


Expand


46-2M+4M=60


Simplify


2M=60-46


Simplify


M=14/2


M=7


substitute back in


C=23-7


C=16A building holds chickens and mice. Jen counted 60 feet and 23 heads. How many of each animal are there?
let x be the number of mice


let y be the number of chicken





there are 23 heas including both mice and chicken


x + y = 23





mice have 4 legs


chicken have 2 legs


there are total of 60 legs


4x + 2y = 60








-2(x + y = 23)


4x + 2y = 60





-2x - 2y = -46


4x + 2y = 60


------------------


2x = 14


x = 7








y = 23 - 7


y = 16








7 mice and 16 chickens