how many pigs and hens are there in a barnyard if there are 13 heads and 34 legs?

Question

please show me how you got your solution, it will help me with my homework

Answer 1

If x= number of heads with two legs
and y= number of heads with 4 legs
then

x+y= 13 total heads (see what the problem statement says)

and then 2x equals number of legs from a 2 legged head
and then 4X equals number of legs from a 4 legged head

Then 2x+4y= 34 legs total from 2 legged heads and 4 legged heads

The two simultaneous equations to solve are then

x+y=13
2x+4y=34

How to solve this? Use substitution meaning

if x+y=13 then y=13-x (hope you got that by adding -x to both sides of the equation. Remember that if you do the same thing to bothe sides then the two sides are still equal)

Sunstitute y=13-x into 2x+4y=34

2x + 4(13-x)=34 then
2x+ 4(13) - 4x = 34 then
2x + 52 - 4x = 34 then
2x-4x= 34-52 or
-2x= -18 or
2x=18 or
x=18/2 or
x=9

Substituting x into one of the equations such as x+y= 13
9+y=13 or y=4

Which then means there are 9 hens (one head with two legs) and 4 pigs (one head with 4 legs).

Got it?

Answer 2

Four pigs (4 x 4) and nine hens (9 x 2). 13 heads and (16 + 18) 34 legs.

Answer 3

4 pigs and 9 hens

Answer 4

none.

1 alien with 13 heads and 34 legs

Answer 5

4 pigs, 9 hens.

Answer 6

If your teacher was talking about varables, than answer looked for would be undeterminable.

Answer 7

42 - the answer is always 42