We have 48 herds both hens and cows with total of 148 legs.how many hens are in the herds

Answer 1

Let's denote the number of hens as H and the number of cows as C.
We know that every hen has 2 legs and every cow has 4 legs.
So, the total number of legs can be calculated as: 2H (legs of hens) + 4C (legs of cows).
It is also given that there are 48 herds in total, so we can write the following equation:
H + C = 48 (Equation 1)
Furthermore, we're given that the total number of legs is 148, so we can write the following equation:
2H + 4C = 148 (Equation 2)
We can now solve this system of equations by eliminating one variable.
Multiplying Equation 1 by 2:
2H + 2C = 96 (Equation 3)
Subtracting Equation 3 from Equation 2 to eliminate H:
(2H + 4C) - (2H + 2C) = 148 - 96
2C = 52
Dividing both sides by 2:
C = 26
Substituting the value of C into Equation 1:
H + 26 = 48
H = 48 - 26
H = 22

Therefore, there are 22 hens in the herds.