the total number of cows and ducks on a farm is 35.All the cows have 74 more legs than all the ducks.How many cows are there on the farm?

To find the number of cows on the farm, we need to set up a system of equations based on the given information.

Let's assume the number of cows is represented by 'C' and the number of ducks is represented by 'D'.

We are given two pieces of information:

1. The total number of cows and ducks is 35:
C + D = 35 (Equation 1)

2. All the cows have 74 more legs than all the ducks:
4C = 2D + 74 (Equation 2)

Equation 1 represents the total count of animals, while Equation 2 represents the relationship between the number of legs.

Now, we can solve this system of equations to find the value of 'C' (the number of cows).

First, let's rearrange Equation 2 to isolate D:
4C = 2D + 74
2D = 4C - 74
D = (4C - 74) / 2

Now, substitute D in Equation 1 with the above expression:
C + (4C - 74) / 2 = 35

Simplifying this equation will give us the solution for C.

Now, we can use algebraic methods such as combining like terms, simplifying fractions, and solving for C:

(2C + 4C - 74) / 2 = 35
(6C - 74) / 2 = 35
6C - 74 = 2 * 35
6C - 74 = 70
6C = 70 + 74
6C = 144
C = 144 / 6
C = 24

Therefore, there are 24 cows on the farm.