Marbles come in two sizes: 2-inch diameter and 3-inch diameter. The 3-inch diameter marbles cost 50 cents more than the 2-inch marbles. Jorge buys 20 3-inch marbles for science project and spends exactly $16. Find the cost of a 2-inch marble.
Let x be the cost of a 2-inch marble in cents.
The cost of a 3-inch marble is x + 50 cents.
Jorge spends 20 * (x + 50) cents on 3-inch marbles.
20 * (x + 50) = 1600
Dividing both sides by 20, we get x + 50 = 80
Then x = 80 - 50 = <<80-50=30>>30
The cost of a 2-inch marble is $0.30. Answer: \boxed{30}.