Question

In a pen of goats and chickens there are 25 heads and 90 feet. How many goats and chickens are in the pen.

Answer 1

5 chickens, 20 goats

Explanation:

We can set up two equations and use substitution

There are 25 total goats and chickens, so

`G + C = 25`

Goats have 4 feet and chickens have two, so

`4G + 2C = 90\\`

By solving for G in the first equation,

`G = 25 - C\\`

We can now use substitution,

`G = 25 - C\\4G + 2C = 90\\4(25 - C) + 2C = 90\\100 - 4C + 2C = 90\\-2C = -10\\C = 5\\`

We have 5 chickens, so we have 20 goats.

Let's double check:

`5(2) + 20(4) = 90\\10 + 80 = 90\\90 = 90\\`

It checks out!