A farmer saw some chickens and pigs in a field. He counted 45 heads and 146 legs. Determine exactly how many chickens and pigs he saw.

Answers:

17 chickens and 28 pigs

Explanation:

c = number of chickens

p = number of pigs

There are 45 heads, so c+p = 45. This solves to p = 45-c.

Since chickens have 2 legs and pigs have 4, this means there are 2c legs from all the chickens and 4p legs from all the pigs. In total there are 2c+4p legs.

Set this equal to 146 to get the second equation

2c+4p = 146

Then plug in p = 45-c and solve for c

2c+4p = 146

2c+4(45-c) = 146

2c+180-4c = 146

-2c+180 = 146

-2c = 146-180

-2c = -34

c = -34/(-2)

c = 17

There are 17 chickens.

p = 45-c

p = 45-17

p = 28

And there are 28 pigs.

Check:

c+p = 17+28 = 45 heads

2c+4p = 2*17+4*28 = 34+112 = 146 legs

The answers are confirmed.

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