A farmer has a certain amount of land that she wants to use for planting two different crops: corn and beans. Let the area designated for corn be denoted as $c$ acres and the area for beans as $b$ acres. The farmer has a total of 120 acres of land. If the area for corn is twice that of the area for beans, how much land is designated for corn and how much for beans?

Set up the equations based on the given information and solve for $c$ and $b$.