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Let's assume that the number of chickens is x and the number of cows is y.
Since a chicken has 2 legs and a cow has 4 legs, we can create two equations based on the given information:
Equation 1: x + y = 30 (the total number of chickens and cows is 30)
Equation 2: 2x + 4y = 82 (the total number of legs is 82)
To solve these equations, we can use the substitution method. First, we solve Equation 1 for x:
x = 30 - y
Substitute this expression for x in Equation 2:
2(30 - y) + 4y = 82
60 - 2y + 4y = 82
2y = 82 - 60
2y = 22
y = 22 / 2
y = 11
Now we can substitute the value of y back into Equation 1:
x + 11 = 30
x = 30 - 11
x = 19
Therefore, there could be 19 chickens and 11 cows on the farm.