A farmer kept track of his cows and chickens by counting both the legs and the heads, if he counted 78 legs and 35 heads, how many cows and how many chicken did he own?

4 w + 2 k = 78

w + k = 35

solve the system for coWs and chicKens

suppose they were all chickens. That would require 35*2 = 70 legs

You have 8 extra legs.
Each chicken you replace with a cow requires 2 extra legs.
So, it looks like 4 of the 35 animals are cows.

You bad

To solve this problem, we can use a system of equations. Let's assume that the number of cows is represented by 'C', and the number of chickens is represented by 'CH'.

1. Determine the total number of legs: In this case, cows have 4 legs and chickens have 2 legs. We can create an equation for the total number of legs using the given information:
4C + 2CH = 78

2. Determine the total number of heads: We can create an equation for the total number of heads using the given information:
C + CH = 35

Now, we have two equations:
4C + 2CH = 78 (Equation 1)
C + CH = 35 (Equation 2)

We can solve this system of equations using substitution or elimination.

Let's solve by substitution:
1. Rearrange Equation 2 to express C in terms of CH:
C = 35 - CH

2. Substitute this expression for C in Equation 1:
4(35 - CH) + 2CH = 78
140 - 4CH + 2CH = 78
-2CH = -62

3. Divide both sides by -2 to isolate CH:
CH = (-62) / (-2)
CH = 31

4. Substitute the value of CH back into Equation 2 to find C:
C + 31 = 35
C = 35 - 31
C = 4

Therefore, the farmer owns 4 cows and 31 chickens.