Question

while walking in the country, you count 28 heads and 78 feet in a field of pigs and chickens. how many of each animal are there?

Answer 1

There are 11 pigs and 17 chickens.

Explanation:

Lets let

p = number of pigs

c = number of chickens

Assuming each animal has only one head, then

p + c = 28

And assuming that pigs have four feet and chickens have two feet:

pig feet = 4p

that is, 4 feet for each pig, and



chicken feet = 2c

right? two feet per chicken.



All the feet are:

4p + 2c = 78

Now we have two equations and two unknowns, so we can solve this "system of equations". You can use substitution or elimination method (or even graphing or matrices) I will run through elimination method.

Multiply p+c=28 times -2.

-2p + -2c = -56

then add the whole equation to the other equation. Do this adding vertically, from top to bottom.

-2p + -2c = -56

4p + 2c = 78

_____________

2p = 22

Divide by 2 to solve

p = 11

There are 11 pigs.

Remember,

p + c = 28

11 + c = 28

subtract 11

c = 17

There are 17 chickens.