How many pigs and how many chickens?

Question

There are 100 heads and 270 legs, how may chickens and how many pigs r there?

Answer 1

Let x be the number of pigs and y the number of chickens.
x+y=100 (this is the number of heads, and both animals have only one head each).
4x+2y=270 (because pigs have 4 legs and chickens have 2 legs each)
Divide the second equation by 2 to get the lowest common denominator, so you have:
2x+y=135
Enlarge the second equation so that you can equate both sides:
x+x+y=135 AND x+y=100
Subtract (x+y) from one side of the equation and 100 from the other, so you are left with:
x=35
If x = 35, then y must be 65, to make up the total of 100 animals.
So you have 35 pigs and 65 chickens.

Then re-check to make sure the answer is correct:
35 pigs would make 35x4 legs, or 140.
65 chickens would make 65x2 legs, or 130.
130+140 = 270!!

Answer 2

Let p be the number of pigs and c be the number of chickens. You'll end up with 2 equations:

4p + 2c = 270 (4 legs per pig, 2 per chicken)

p + c = 100 (1 head for both)

So p = 100 - c. Subtitute that in the first equation and you get:

4(100 - c) + 2c = 270

c = 65

Plug that into the seconed equation and you get p = 35.

So there are 65 chickens and 35 pigs.

Answer 3

35 pigs 35 times 4 is 140

65 chickens 65 times 2 is 130

140+130 is 270

65+35= 100

Answer 4

65 chickens 35 pigs

Answer 5

35 pigs and 65 chickens

Answer 6

35 pigs and 65 chickens

Answer 7

35 pigs and 65 chickens

Answer 8

Make the question into a set of equations.

Let P=pigs
Let C=chickens.

P + C = 100 <---gets the number of each animal.

P(4) + C(2) = 270 <--gets the number of legs for each.

Then solve by substitution.

Answer 9

...let x= #of pigs, y= #of chickens
x + y = 100
4x + 2y = 270...use elimination and voila!!!

x= 35 , y=65 , 35 pigs, 65 chickens

Answer 10

100