a farmhaschickensandcows. youaskthefarmerhowmanychickenshehas,andhowmanycowshehas.thefarmertellsyouhehas28healthyanimals,andtheyhaveatotalof64legs.howmanycowsdoeshe have? how many chickensdoeshehave?

Question

show ALL work and determine if substitution or elimination.

Answer 1

B=Chicken --> 2 legs

C=Cow --> 4 legs

B + C = 28 ---> this means that cows and chickens together are the total amount of farm animals. Cows + Chickens = 28

2B + 4C = 64 ---> this means that each chicken * 2 = how many chicken legs there are and each cow * 4 = how many cow legs there are.

This would be easiest to solve with elimination although both work just as well. Just preference. But since we have the equations and variables lined up under one another, it'll be less work and less writing to use elimination.

Solving process for elimination:

1) line up the equation so that B's are on top of each other, C's are on top of each other and so are the numbers

B + C = 28

2B + 4C = 64

2) Multiply the top equation by either -2 (to cancel out B) or by -4 (to cancel out C)

I will choose -2 because that way we don't have to deal with negative numbers.

-2*( B + C = 28 )

-2B + (-2C) = -56

3) Add the new equation to the second equation.

-2B + (-2C) = -56

+

2B + 4C = 64

-----------------------------

0 + 2C = 8

4) solve for C

C = 4

5) Plug C back into either equation to get B. I'll plug it back into B + C = 28 because that seems like it has the least steps to solve with.

C=4

B + (4) = 28

-4 -4

-------------------

B = 24

6) write down your answer

There are 24 chickens and 4 cows.

Hope this helps! If you have any more questions or need more clarification feel free to write a comment and I'll answer as soon as possible. Thanks! :^)

~Anika

Answer 2

Let x = number of cows and y = number of chickens.

Cows have 4 legs and chickens have two legs.

x+y = 28 --> y = 28-x

4x+2y = 64

4x + 2(28-x) = 64

4x + 56 - 2x = 64

2x = 8

x = 4 cows

y = 28-4 = 24 chickens.