From the ideal gas equation, the number of moles of the first gas is n1=RT1P1V1 and the number of moles of the second gas is n2=RT2P2V2.
For the mixture, the total number of moles is n=n1+n2.
Applying the ideal gas equation for the mixture:
PV=nRT
T=nRPV
Substituting the values of n1 and n2:
T=(RT1P1V1+RT2P2V2)RPV
T=T1P1V1+T2P2V2PV
T=P1V1T2+P2V2T1T1T2PV
Answer: T1T2PV/(T2P1V1+T1P2V2)