To solve this, it is helpful to set up an equation that reductions and additions of the games. The equation would be:
27 = 1/2v + 3
In this equation, v = the original number of video games. The 1/2 signifies Casey selling his games, and the + 3 shows Casey buying three more.
If we subtract 3 from both sides, we see that 1/2v = 24. Finally, we can multiply each side by 2 to isolate the variable, v, and we get v = 48.
Therefore our final answer is 48 video games.
Hope this is helpful!