Final answer:
The total number of legs of the cows and chickens combined is represented by 128, and the total number of heads is represented by 48. By setting up a system of equations, we can solve for the number of cows and chickens. Using the substitution method, we find that there are 16 cows and 32 chickens on the farm.
Step-by-step explanation:
Part A:
In the problem, 128 represents the total number of legs of the cows and chickens combined. Since cows have 4 legs and chickens have 2 legs, let's represent the number of cows as 'C' and the number of chickens as 'Ch'.
Now, we can set up an equation: 4C + 2Ch = 128.
Part B:
48 represents the total number of heads of the cows and chickens combined. Since each animal has one head, the number of cows and chickens together is represented by 'C + Ch'.
The equation for this is: C + Ch = 48.
Part C:
We have two unknowns (C and Ch) and two equations. We can set up a system of equations:
4C + 2Ch = 128 (Equation 1)
C + Ch = 48 (Equation 2)
Part D:
To solve this system, we can use the method of substitution. From Equation 2, we can isolate one of the variables:
C = 48 - Ch
Now we substitute this value of C into Equation 1:
4(48 - Ch) + 2Ch = 128
After simplifying, we get:
192 - 4Ch + 2Ch = 128
-2Ch = -64
Ch = 32
Substituting this value of Ch back into Equation 2, we can find the value of C:
C + 32 = 48
C = 16
Therefore, there are 16 cows and 32 chickens on the farm.