if the farmer count his hens and cow by 78 legs&35 heads.how many cow has he?

Question

math logic, show the mathematical solution to the problem.

Answer 1

2H+4C=78 [1]
H+C=35 [2]
so 2H+2C=70 [3]
so [1] - [3] gives
2C = 8
so C=4 and hence H=31
.

Answer 2

Assuming no animal is wise-a__ing and wearing two heads or is a cripple, we can write an equation for heads and legs. If X is the number of cows,
(35-X) is the number of hens. Then
2* (35-X) + 4* X = 78 leg equality
Solving, X=4.

There is another way to do this, if there were all chickens, you would have 35 heads and 70 legs, which is pretty close to what you have. Conceptually, you trade a chicken for a cow, which keeps the head-count constant, but increases the leg count by 2.

Answer 3

Let h = # of hens
Let c = # of cows

Since each cow and each hen had 1 head, and there are 35 animals:

c + h = 35

Since a cow has 4 legs, and a hen has 2, and there are 78 legs total:

4c + 2h = 78

Now you have 2 equations, and 2 unknowns. The equation is therefore solveable by substitution or other means.

c + h = 35 (multiply each side by -2)
-2c -2h = -70
4c + 2h = 78 (add to 2nd equation)

2c = 8
c =4
h = 31

4 cows, 31 hens

Answer 4

1 hen=2 legs
1cow=4legs
let num of cows=c & num of hen = h

from 78 legs: 4c+2h=78
2c+h=39

from 35 heads: c+h=35

solving the 2 simultaneous eqn: c=4 & h=31

==> 4 cows & 31 hens

Answer 5

nicely that relies upon on whether the hens or cows are defected with extra beneficial than their ideal quantity of legs or in the event that they have 2 heads. There are cows and hens obtainable right this moment with that concern. One farmer has 3 cows on his farm with 5 legs each and every. That exhibiting became into on television some months in the past.

Answer 6

Simple algebra. Legs: 2H + 4C = 78; heads: H + C = 35. Divide the first equation by 2 to get H + 2C = 39, which immediately gives C = 4. Hence, H = 31.

Answer 7

[4x + 2y = 78] [x + y = 35] (where x = cows, y = chickens)
y = 35 - x
4x + 2(35-x) = 78 simplify
4x + 70 - 2x = 78
4x - 2x = 8
2x = 8
x=4

Answer 8

Yep, 4 cows it is!


Oh my god I thought it was a really simple problem til I saw those equations, now I have a headache!!!

Answer 9

one cow 34 hens

Answer 10

4 moo moos