Question

There are 13 animals in a barn. Some are Chickens and some are Pigs. Altogether

they have 40 legs. How many of each animal are in the barn?
There are 5 pigs and 8 chickens.
There are 8 pigs and 5 chickens.
There are 7 chickens and 6 pigs.
There are 7 pigs and 6 chickens.

Answer 1

Answer: i could figure out there were 7 pigs

Explanation:

Answer 2

Ahh! What a classic: Systems of Equations!

So, if you don't know what a system of equations is, its basically two equations with two variables combined into a system.

So, let x=# of pigs

And also, Let y=# of chickens

Let's make our first equation!

`13=x+y`

This is because there are 13 animals in a barn.

So then, knowing that a pig has 4 legs and a chicken 2:

`40=4x+2y`

This is because there are 40 legs in total, and we multiply the variable because that's how many legs each creature has.

So, here is our system!

`\left \{ {{x+y=13} \atop {4x+2y=40}} \right.`

Through Substitution (the inputting of something instead of a variable):

`x+y=13\\x=13-y`

Then, we input it into the next equation:

`4(13-y)+2y=40\\52-4y+2y=40\\-2y=-12\\y=6`

This means that there are 6 chickens, and by inputting it into the first equation:

`x+6=13\\x=7`

So there you have it!

FYI there are 6 chickens and 7 pigs.

Hope this helps!

P.S. Stay Safe!