Problem: There are hens and goats in a farm, with a total of 50 animals. When counting their legs, there are a total of 144 legs. How many hens and how many goats are there?

Solution:

To solve this problem, we need to use algebraic equations to represent the given information. Let's assume that the number of hens is "x" and the number of goats is "y."

1. Write the equations for the total number of animals and legs:

x + y = 50 (total number of animals)
2x + 4y = 144 (total number of legs)

2. Simplify the equations by solving for one variable in terms of the other:

x = 50 - y (from equation 1)
2(50 - y) + 4y = 144 (substitute x into equation 2 and simplify)

3. Solve for y:

100 - 2y + 4y = 144
2y = 44
y = 22

4. Calculate the number of hens:

x = 50 - y
x = 50 - 22
x = 28

Therefore, there are 28 hens and 22 goats in the farm.

Explanation:

To solve this problem, we need to use algebraic equations to represent the given information. We know that the total number of animals is 50, so we can write the equation x + y = 50, where x is the number of hens and y is the number of goats.

We also know that the total number of legs is 144. Since hens have two legs and goats have four legs, we can write the equation 2x + 4y = 144.

We can simplify the equations by solving for one variable in terms of the other. Solving for x in the first equation gives x = 50 - y. Substituting this into the second equation gives us 2(50 - y) + 4y = 144. Simplifying this equation gives us 100 - 2y + 4y = 144, which simplifies to 2y = 44. Solving for y gives us y = 22.

Finally, we can calculate the number of hens by substituting y into the first equation: x = 50 - y = 50 - 22 = 28. Therefore, there are 28 hens and 22 goats in the farm.

Let no. of hens be x and no. of cows be y. For heads the equation is

x + y = 50 (head count is 50)

For legs the equation is

2x + 4y =144 (2 legs of hen and 4 legs of cow assuming that none are missing any limbs)

From head count equation

y = 50 - x

substituting this in leg count equation we get

2x + 4(50 - x) = 144

2x + 200 - 4x = 144

-2x = 144 - 200

-2x = - 56

x = 28

Substituting in headcount equation we get

y = 50 - 28

So y = 22

So there are 28 hens and 22 cows on the farm.