Question

Between the cows and the chickens , there are 16 eyes and 26 feet. How many chickens does she have and how many cows?

Answer 1

Answer:

Step-by-step explanation:

Looks like a system of equation type situation.  To figure it out you wan to set up equations for each thing we know, so eyes and feet.  First you want to make sure you have how many eyes and feet cows and chickens have.    of course they each have 2 eyes while cows have 4 feet and chickens have 2.  Now we can set up the equations.

Let's start with eyes.  16 total and cows will contribute 2 each and chickens will as well.  Another way to write this is 16 = 2o + 2h, where o represents the number of cows and h represents the number of chickens.  If this doesn't make sense maybe plugging in some values to see how it all works.  if there are 3 cows and 4 chickens how many eyes are there?  2*3 + 2*4 = 14, so 14 eyes total.

Similarly for feet we can set up 4o+2h and if you plug in however many cows and chicens there are you'd get the number of legs.  and the problem tells us this equals 26, so 4o+2h = 26

Now the math part, using both equations  we can solve for o and i.

2o+2h=16

4o+2h=26

THere are a few ways to do this.  if you treat o and h like x and y, you could graph both equations and see where they intersect.  Doing this you could make either variable x, so then the other would be y, but you have to make sure all os become the same one and all hs do as well.  

I think it would be easier in general to make one equation equal one of the variables, then replace it in the other equation.  I will show you this method.  First, I want to take the first equation and set it equal to o.

2o+2h=16 divide it by 2

o + h = 8 we want o by itself so subtract h from both sides

o = 8 - h and there we go.

Now we want to replace o in the other equation with this.

4o+2h=26 replace o with 16-h

4(8-h) + 2h = 26  Now just solve for h

32 - 4h + 2h = 26

-2h = -6

h = 3

Now we plug THIS back into the first one.  

o = 8 - h

o = 8 - 3

o = 5

And that should solve it.  with 5 cows and 3 chickens how many eyes and feet are there?

16 eyes and 26 feet, which is exactly what we want.  

Do keep in mind this won't always work, sometimes there is no answer, or every answer works.  You will be able tot ell through this process though.