Difficult HVAC PE Practice Problem

[Remusco]

TL;DR Summary: Determine the wet bulb temperature of air entering a room when the dry-bulb temperature is given.

This is the hardest HVAC PE practice problem I've attempted. Can someone show me how they would approach this?
The goal is to find Twb leaving the cooling coil as shown in the image below:

 

[russ_watters]

I've moved this to homework help because it is a homework type problem.

At first glance this looks like a straightforward psychometric mixing and cooling problem, unless there is a trick that reveals itself after solving the basic problem. Please show us your attempted solution.....you can do a psychrometric mixing calculation, right?