A farm has ducks and goats. There are 77 animals in total. The total number of legs is 224. How many ducks are there?

Let $D$ be the number of ducks.
Let $G$ be the number of goats.

Each animal has 1 head. So, the total number of heads is:

Ducks have 2 legs each, and goats have 4 legs each. So, the total number of legs is:

From Equation 1, express $G$ in terms of $D$:

Substitute this expression for $G$ into Equation 2:

The number of ducks is 42.

The correct option is (A).

The number of ducks is $\boxed{\text{42}}$.