We can start by setting up an equation to represent the problem. We want to find the value of t that makes c equal to $20:
$20 = 12.70 + 0.14t
Subtracting 12.70 from both sides, we get:
$7.30 = 0.14t
Dividing both sides by 0.14, we get:
t = 52.14
Therefore, Mike can send and receive 52 text messages for $20. However, since he cannot send or receive a fraction of a text message, the actual number of messages he can send and receive for $20 is 52.
So the answer is D. 52.