Question

A farmer saw some chickens and pigs in a field. He counted 60 heads and 176 legs. How many chickens and how many pigs did the farmer see ?

Answer 1

He saw 32 chickens and 28 pigs.

Let p be the number of pigs and c be the number of chickens.

Each pig has 1 head and each chicken has 1 head; this gives us the equation
1p + 1c = 60 or
p + c = 60

Each pig has 4 legs and each chicken has 2 legs; this gives us the equation
4p + 2c = 176

In the first equation, we will isolate c by subtracting p from both sides:
p + c - p = 60 - p
c = 60 - p

We will substitute this into the second equation:
4p + 2(60 - p) = 176

Using the distributive property, 
4p + 2*60 - 2*p = 176
4p + 120 - 2p = 176

Combining like terms,
2p + 120 = 176

Subtract 120 from each side:
2p + 120 - 120 = 176 - 120
2p = 56

Divide both sides by 2:
2p/2 = 56/2
p = 28

There are 28 pigs.

Substitute this into the first equation:
p + c = 60 
28 + c = 60

Subtract 28 from each side:
28 + c - 28 = 60 - 28
p = 32