An automobile gasoline tank holds 21 kg of gasoline. when the gasoline burns, 84 kg of oxygen is consumed, and carbon dioxide and water are produced. what is the total combined mass of carbon dioxide and water that is produced?

This is as straightforward as it gets. If however you need to determine how much of each product is produced, then the balanced equation is a must.

Usually, gasoline is expressed as octane in combustion reactions, which means that the balanced equation for its combustion is

2C8H18+25O2→16CO2+18H2O

But, like I've said, for the combined mass of the products all you really need to know is the combined mass of the reactants.

Addendum

Let's say you want to know exactly how much of each compound is formed. In this case, you must check for a limiting reagent. The number of moles of octane is

21⋅103 g⋅1 mole octane114.0 g=184.2 moles

The number of moles of oxygen is

85⋅103 g⋅1 mole O232.0 g=2656 moles

According to the mole ratio between these two, each 2 moles of octane need 25 moles of oxygen, so

noxygen that reacts=noctane⋅252=2303 moles , which means that octane is the limiting reagent. The actual mass of oxygen that reacts is

2303 moles⋅32.0 g1 mole=73.7 kg

This means that the combined mass of the produced water and carbond dioxide is actually

21 kg+73.7 kg=94.7 kg

85 kg−73.7 kg=11.3 kg of oxygen will not react. If you want to count this oxygen as well, the total combined mass of the products will again be 106 kg .