Can this problem's second half be solved by using enthalpies and a control volume around the room, rather than considering a control volume around the coil looking at heat loads of the room+the outside air?
Using Control Volume of the Room:
Mass leaving coil*enthalpy leaving coil + LH+SH= mass leaving room*enthalpy leaving the room, solving for the enthalpy leaving the coil to find Twb? LH and SH given, enthalpy leaving the room and mass flow rate leaving the room using the psychrometric chart at 78da,45%rh (specific volume = ~14.2ft^3/lbm, h= ~40). In that way, I have a mass flow rate of 15710lbm/hr, and the mass leaving coil*enthalpy leaving coil = 331874btu/hr. Using the same mass flow rate of 15710 lbm/hr, i got an enthalpy of the air leaving the coil as 21.1 btu/lbm. And then given that and our 55da, used the psychrometric chart again to find the wet bulb of 51, same as the solution guide.
By doing this, you don't have to deal with the outside air, but just the mixture of air at a constant flow rate.
I get the same answer as NCEES solutions, and I don't think i'm making any wrong assumptions.
In the NCEES way, am I correct in that we drawing a control volume around the coil, with a heat removal of the load of the room+the 700cfm from the outdoors, since we know the heat that must be removed 2900cfm (the SH+LH)? Essentially splitting up the mixture into outside heat load and room heat load, and then our final state (leaving the coil) is the combined. Am I understanding that right? I think going about it the way I did takes longer, but is more intuitive for me. I have a power plant/boiler background, and not much HVAC experience, so some of these HVAC topics are a new way of thinking for me.