What is the percentage change in the temperature?

Question

The temperature of an ideal gas varies directly with its pressure and inversely with the number of molecules in the vessel. If the pressure is increased by 5% and the number of molecules is decreased by 10% what is the percentage change in the temperature? State whether it increases of decreases and five the percentage change to the nearest .1 percentage.

Answer 1

T= k* p/N so
dT = k dp/N -k *p/N^2*dN
dT/T=dp/p -dN/N
dp/p=0.05
dN/N=-0.10 so
dT/T = 0.15 increases 15%