Question

A farmer saw some chickens and pigs in a field. He counted 60 heads and 176 legs. Find out exactly how many chickens and how many pigs he saw. Show your strategies and explain how you solved the problem.

Answer 1

Let's assume

number of chickens =c

number of pigs =p

He counted 60 heads

each pig has one head and each chicken has one head

so, we get equation

`1*c+1*p=60`

`c+p=60`

He counted 176 legs

Chicken has two legs

pigs has four legs

so, we get equation as

`2*c+4*p=176`

`2c+4p=176`

so, we get two equations as

`c+p=60`

`2c+4p=176`

we can eliminate any one variable from first equation and plug that in second equations and then we can solve for c and p

solve for c

`c=60-p`

plug this into second equation

`2(60-p)+4p=176`

now, we can solve for p

`120-2p+4p=176`

`2p=176-120`

`2p=56`

`p=28`

now, we can solve for c

`c=60-28`

`c=32`

so,

number of chickens are 32

number of pigs are 28...............Answer