Question

Kelly went to visit her uncle's farm. She noticed that the farm has a large number of cows and chickens. She counted 268 legs and 119 heads. How many cows and how many chickens are on Kelly's uncle's farm?

Cows:

Chickens:

Answer 1

She counted 268 legs...and 119 heads

cows have 4 legs...chickens have 2
each only has 1 head so....you have a system of equations

let 'c' = chicken and 'w' = cow


2c + 4w = 268
c + w = 119

can you solve this?

Answer 2

It cannot be solved.

Answer 3

And how can I do that?

Answer 4

2c + 4w = 268
c + w = 119

lets solve that second equation....for the variable 'w'

Answer 5

c + w = 119

to solve for 'w' we subtract 'c' from both sides

w = 119 - c

Answer 6

could I do
c + w = 119
-w -w
c = 119-w
it's confusing.

Answer 7

Well yes okay...lets do it your way :) that is how you would solve for 'c'

Answer 8

but then what could I do? there's still "w" and if I were to divide c by 119 would that give me anything over c/119?

Answer 9

you have found that c = 119 - w

right?

Now go back to the FIRST equation...

2c + 4w = 268

plug in what you found for 'c'

Answer 10

*We will solve for 'w' very soon :) *next step actually! :)

Answer 11

so...
2 (119-w) +4w =226?

Answer 12

238-2w +4w=226
-238 -238
-2w +4w = -212
2w= -212
w= -106?

Answer 13

Actually this is a weird one...but one thing you did wrong above was

what is 226 - 238...this = -12 correct?

so theoretically we would have

2w = -12

w = -6

Let me do this myself real quick okay?

Answer 14

ahh nvm....just a simple typo above...where you said

"so...
2 (119-w) +4w =226?"

226 should be 268 :)

Answer 15

lol
ohhh ok
xD

Answer 16

haha I was like...THIS IS IMPOSSIBLE!! haha

okay so go on from

2 (119-w) +4w =268

Answer 17

so it would be
238-2w +4w= 268
-238 -238
2w=30
w=15

Answer 18

there we go! lol

so we have 15 cows.....now...we solve for 'c'

remember

c + w = 119

we now know w = 15 so...

c + 15 = 119

what is 'c' ?

Answer 19

wouldn't c equal 104?
:D

Answer 20

it would indeed!

now check to make sure it is correct

take the second equation

2c + 4w = 268

plug in your values for 'c' and 'w' to make sure it comes out correct! :)

Answer 21

2(104)+ 4(15)=268
208+60
omggg <333

Answer 22

haha there you go! :D

see, easy! :)

Answer 23

lol! thank you so much (: <3

Answer 24

anytime! :)