We can use proportions to solve the problem:
Let x be the amount of food (in cups) that a 50 pound dog eats in one day.
Since the amount of food eaten is directly proportional to the weight of the dog, we can set up the following proportion:
20 pounds / 3 cups = 50 pounds / x cups
To solve for x, we can cross-multiply:
20 pounds * x cups = 3 cups * 50 pounds
20x = 150
x = 7.5
Therefore, a 50 pound dog would eat approximately 7.5 cups of food in one day, assuming that the amount of food eaten is directly proportional to the weight of the dog.