J.R. S. answered 10/06/18
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This is an example of Dalton's Law of Partial Pressure. The total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the gases in the mixture.
PP N2O = 425 torr
PP O2 = 786 torr
Ptotal = 425 torr + 786 torr = 1211 torr
mole fraction N2O = 425/1211 = 0.35
mole fraction O2 = 786/1211 = 0.65
Ratio of N2O to O2 = 0.35/0.65 = 0.54
If you wanted to do this more simply, you could just take the ratio of 425/786 = 0.54 since the partial pressure is proportional to the moles.