There are a total of 50 ducks and goats in a farm. They have 154 legs altogether. How many ducks are there?

4 g + 2 d = 154

g + d = 50

4 g + 2 d = 154
2 g + 2 d = 100
--------------- subtract
2 g = 54
You can take it from there I think.

To determine the number of ducks, we need to set up a system of equations using the information given in the problem.

Let's denote the number of ducks as 'd' and the number of goats as 'g'.

From the problem, we know there are a total of 50 ducks and goats, so we can write the first equation as:
d + g = 50

We also know that the total number of legs is 154. Since ducks have two legs and goats have four legs, we can write the second equation as:
2d + 4g = 154

To solve this system of equations, we can apply various techniques like substitution or elimination. However, let's use the substitution method for this example.

From the first equation, we can solve for 'g' in terms of 'd' by subtracting 'd' from both sides:
g = 50 - d

Substituting this expression for 'g' into the second equation, we get:
2d + 4(50 - d) = 154

Simplifying the equation:
2d + 200 - 4d = 154

Combining like terms:
-2d = -46

Dividing both sides by -2:
d = -46 / -2
d = 23

Therefore, there are 23 ducks in the farm.