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?

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