The Razorback t-shirt shop makes $ 23 dollars off each t-shirt sold. During the Arkansas and Texas tech game they made $ 230 by selling t-shirts. How many t-shirts did they sell?
$23$ dollars off each t-shirt sold means that the shop sells each t-shirt for $23$ dollars. 

$230$ dollars from selling t-shirts during the game means that the shop sold $230$ dollars worth of t-shirts during the game. 

We can write this as follows: 
$$23t = 230$$
$$t = \frac{230}{23}$$
$$t = 10$$

This means that the shop sold $10$ t-shirts during the game.