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. Ther…

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asked Oct 20, 2021 194k views

2 Answers

Terrybozzio · Answer 1 · 2021-10-24T03:28:52+0000

Answer:

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!