Using the #3.00" L"# bottle, empty mass is #1.70" kg"#, and #4.55" kg"# full mass, we can compute the mass density of the wine:
#((4.55-1.70)" kg of wine")/(3" L of wine")#
We can multiply that by #11%# converted to a decimal #0.11# to obtain the mass of alcohol (in kg) per Liter:
#((4.55-1.70)cancel(" kg of wine"))/(3" L of wine")(0.11" kg of alcohol")/(1cancel(" kg of wine"))#
We convert the #400.0" ml of wine"# to #0.4000" L of wine"# per glass:
#((4.55-1.70)cancel(" kg of wine"))/(3cancel(" L of wine"))(0.11" kg of alcohol")/(1cancel(" kg of wine"))(0.4000cancel(" L of wine"))/(1" glass of wine")#
Please observe that the units that have not cancelled are "kg of alcohol per glass of wine".
We need to convert to oz of alcohol so we use the conversion factor #(16" oz of alcohol")/(0.4536" kg of alcohol")#:
#((4.55-1.70)cancel(" kg of wine"))/(3cancel(" L of wine"))(0.11cancel(" kg of alcohol"))/(1cancel(" kg of wine"))##(0.4000cancel(" L of wine"))/(1" glass of wine")(16" oz of alcohol")/(0.4536cancel(" kg of alcohol"))#
Please observe that the units that have not cancelled are "oz of alcohol per glass of wine", therefore, we can done with the conversion and we only need to do the arithmetic:
#((4.55-1.70)(0.11)(0.4000)(16))/(3(0.4536))= (1.47" oz of alcohol")/"glass of wine"#
