We have 48 herds both hens and cows with total of 148 legs.how many hens are in the herds
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.
Let's assume that each cow has 4 legs and each hen has 2 legs.
Let's represent the number of cows as "c" and the number of hens as "h."
Based on the given information, we can form the following equations:
c + h = 48 (Equation 1)
4c + 2h = 148 (Equation 2)
To solve this system of equations, we can use the method of substitution or elimination. Let's use substitution:
From Equation 1, we can express "h" in terms of "c" as h = 48 - c.
Substituting this value of "h" in Equation 2, we get:
4c + 2(48 - c) = 148
Simplifying the equation:
4c + 96 - 2c = 148
Combining like terms:
2c + 96 = 148
Subtracting 96 from both sides:
2c = 52
Dividing both sides by 2:
c = 26
Now we can calculate the number of hens by substituting the value of "c" back into Equation 1:
26 + h = 48
Subtracting 26 from both sides:
h = 22
Therefore, there are 22 hens in the herd.