Question

There are 21 animals on Farmer Cole’s farm — all sheep and chickens. If the animals have a total of 56 legs, how many of each type of animal lives on his farm? Write a system of equations, and use the equal values method to solve it.

Answer 1

sheep usually have 4 legs each

chickens usually have 2 legs each

if c=number of shep and s=number of chickents, then c+s=21

total legs is 56, so 2c+4s=56

system of equations is c+s=21 and 2c+4s=56

equal values method? why do they have to keep changing names, it doesn't sound like subsitution so I'm assuming they mean linear combinations

c+s=21

2c+4s=56

multiply first equation by -2 and add to 2nd equation

-2c-2s=-42

2c+4s=56 +

0c+2s=14

2s=14

divide by 2

s=7

sub back

c+s=21

c+7=21

c=14

14 chickens and 7 sheep