It cost Deion $13.65 to send 91 text messages. How many text messages did he send if he spent $17.40?

Let x be the number of text messages Deion sent.

We can set up the proportion: 13.65/91 = 17.40 / x
Cross multiplying, we get 13.65*x = 91*17.40.
Dividing both sides by 13.65, we get x = (91*17.40) / 13.65.
Calculating, we find x = 115.13
Therefore, Deion sent 115 text messages. Answer: \boxed{115}.