for all you math wizzes out there?

Question

at the fair, the chickens and rabbits were placed under the same tent. the chickens and the rabbits have a total of 360 legs. if there were 105 animals, how many rabbits were there?

Answer 1

Rabbits = 75
Chicken = 30

Solution:
Let the no. of Rabbits be "x"
Let the no. of Chicken be "y"

Then according to the given conditions, we get following two equations

~ x+y=105
~ 4x+2y=360

Solving the two equations simultaneously, you get the answers.

If you need any more help or explaination, you are welcome to mail me anytime.

Good Luck

Answer 2

a way to solve this problem is by simultaneous equations. The steps are the following:

we know that there are 360 legs. We also know that each chicken has 2 legs, and each rabbit has 4 legs. So we can make an equation from this data:
360= 2 legs * amount of chicken + 4 legs * amount of rabbits
=> 360=2x+4y

we also know that there are 105 animals in total. So:
105=x + y

And now we apply simultaneous equations:
105= x + y ---- (multiply the equation by -2)
=> -210=-2x-2y
So:
360=2x+4y
+
-210=2x-2y
-------------------
150=2y
y=75
THERE ARE 75 RABBITS!!

Answer 3

If you hate linear algebra, I offer you another alternative. Assume there are 105 chickens, you will get 210 legs which is 150 legs lesser. It means that there must be 75 rabbits (75 x 2 extra legs than chicken = 150) to compensate for the loss. Minus 75 from 105 you get number of chickens.

Answer 4

c + r = 105
2c + 4r = 360

4c + 4r = 420 - - multiply the top by 4 on both sides
2c + 4r = 360
2c = 60 - - - - - subtract the two equations
c = 30 - - - 30 chickens

30 + r = 105
r = 75 - - - - 75 rabbits.

to check:
2 * 30 + 4 * 75 = 360
60 + 300 = 360 - - - - - -yup, it checks out

This is, of course, assuming that all of the chickens have two legs and the rabbits have four. I've seen three legged chickens.

Answer 5

let x= number of rabbits
y=number of chickens

then:
x + y = 105 (1)

Rabbits have 4 legs while a chicken have 4.

Therefore: 4x + 2y= 360 (2)

re-aranging eqn (1)

x = 105- y substitute this equation to equation (2)

4(105-y) + 2y= 360
420-4y+2y=360
-4y+2y=360-420
-2y=-60
y=30

Substitute y=30 to equation (1)

x + y = 105
x + 30= 105
x= 105- 30
x= 75 rabbits

Answer 6

let chickens be x
rabbits be y

since chicken has 2 legs and rabbits 4 so,
2x + 4y = 360 (1)

Also,
x + y = 105 (2)

Now (1) can rewritten as,
2(x+y) + 2y = 360

From (2)
2*105 + 2y = 360
2y = 360-2*105
2y = 150
y = 150/2
y = 75

From (2)
x + 75 = 105
x = 30

So, chickens are 30 and rabbits are 75

Answer 7

Let x be the number of chickens and y the number of rabbits.
Then, since chickens have 2 legs and rabbits have 4,
2x + 4y = 360
or
x + 2y = 180
also
x + y =105
Subtracting,
y = 75 and x = 30.
There were 30 chickens and 75 rabbits

Answer 8

Seventy five rabbits have 300 legs.
30 chickens have 60 legs .
75+30=105.

Answer 9

X = chickens
Y = Rabits

Assuming the Rabits were still lucky and had all if its feet... ;)

2X + 4Y = 360
X + Y = 105 or X = 105 - Y

2(105 - Y) + 4y = 360

210 -2Y + 4Y = 360
2Y = 150
Y = 75
X = 105 - 75 = 30
Proof:
75 + 30 = 105
2(30) + 4(75) = 360
60 + 300 = 360

Answer 10

75