It cost Josiah $9.75 to send 65 text messages. How many text messages did he send if he spent $28.20?
We can set up a proportion to solve for the number of text messages Josiah sent.
Let x be the number of text messages Josiah sent.
We can set up the following proportion: 9.75/65 = 28.20/x
Cross-multiplying, we get 9.75 * x = 65 * 28.20
Dividing both sides by 9.75, we get x = (65 * 28.20) / 9.75
Simplifying, we get x = 1881/3
Therefore, Josiah sent 1881/3 or approximately 627 text messages. Answer: \boxed{627}.