#### Answer

The ratio of their atomic weights is $1.94$
The atomic weight of phosphorus is $31.0\ g/mol$:

#### Work Step by Step

Initial mass of P: 0.744 g
Final mass of $P_4O_{10}$: 1.704 g
Mass of O: 1.704-0.744 = 0.960 g
Given their proportions (4:10):
P: $0.744/4=0.186\ g$
O: $0.960/10=0.096\ g$
The ratio of their atomic weights is then $0.186/0.096=1.94$
Assuming the atomic weight of oxygen is 16.000 g/mol,
the atomic weight of phosphorus is $1.94\times16=31.0\ g/mol$: