Stoichiometric calculation of composition of a compound
This is an example of a classical method of determining chemical formulas by elemental analysis.
You are not supposed to know the chemical formula of copper oxide neither they are asking you to write a balanced equation. All they are telling you is that
(i) Mass of pure oxide of copper = 3.45 g
(ii) Mass of copper obtained after reduction (we do not need to know the chemical equation) = 2.76 g
Use mass balance, how many grams of oxygen atoms must be there in that oxide?
Now you know the masses of Copper and Oxygen.
Two options
(a) Use mol and find out molar ratios between the two elements
(b) Alternatively, if you do not need to invoke the mole concept ... old school way. Just for trying
Think about the fact that 16 (exactly 16) is the mass unit of 1 oxygen atom. What mass of copper atoms would be associated with 16 units of O if copper's atomic mass is 63.54 units. Use mass balance and some arithmetic.