There are 38 animals at a farm.some are cows some are chickens all together there are 124 legs . How many cows and how many chickens?
legs = 4 cows + 2 * chickens = 124
cows + chickens = 38
so
chickens = 38 - cows
4 cows + 2 (38 - cows) = 124
2 cows = 48
cows = 24
then
chickens = 14
To determine the number of cows and chickens at the farm, we need to use a system of equations. Let's assume the number of cows is 'C' and the number of chickens is 'Ch'.
We know that each cow has 4 legs and each chicken has 2 legs. There are a total of 38 animals at the farm, so we can create the equation:
C + Ch = 38 (Equation 1)
We also know that there are a total of 124 legs, so we can create the equation:
4C + 2Ch = 124 (Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) with two unknowns (C and Ch).
We can solve these equations simultaneously to find the values of C and Ch using various methods such as substitution or elimination. Let's use the substitution method:
From Equation 1, we can express Ch in terms of C:
Ch = 38 - C
Now, substitute this value of Ch in Equation 2:
4C + 2(38 - C) = 124
Simplifying the equation:
4C + 76 - 2C = 124
2C + 76 = 124
2C = 124 - 76
2C = 48
C = 24
We have found that there are 24 cows at the farm.
Now, substitute this value of C back into Equation 1 to find the number of chickens:
24 + Ch = 38
Ch = 38 - 24
Ch = 14
We have found that there are 14 chickens at the farm.
Therefore, there are 24 cows and 14 chickens at the farm.