Density of each temperature?

Question

The air in a hot-air balloon at 754 torr is heated from 13°C to 60.0°C. Assuming that the moles of air and the pressure remain constant, what is the density of the air at each temperature? (The average molar mass of air is 28.8 g/mol.)
13°C

60.0°C

Answer 1

PV=nRT
where
P- is the absolute pressure (Pascals [Pa]),
V- volume [m3] of the vessel containing moles of gas,
n - amount of substance of gas [mol],
R - gas constant [8.314 m3•Pa•K−1•mol−1],
is the temperature in degree kelvin [K].

Some units
1 atm = 101325 Pa
1 atm = 760 torr
at 13 °C air has 1/(28.8 ) moles/ gm

p=m/V

V=nRT/P
m=n(28.8)

p= m/V= nP/[28.8 n R T]
p= 28.8P /[ R T]

For both cases
P= [754/760 ] 101325 Pa= 100525 Pa

Case 1
at 13 °C T= 273.15 +13=286 °K
p= 28.8 P/[R T]
p=28.8 x100525/[ 8.314 x 286]=1.220 kg/m^3
Case 2
at 60 °C T= 273.15 + 60.0=333°K
p= 28.8 P/[R T]
p=28.8 x100525/[ 8.314 x 333]=1050 kg/m^3