The question wants the final answer in volume (mL), but gives you information in mass (g), so we will first calculate the total mass of the soft drink then convert mass to volume using density.
We are told that 10.5% of the solution equals 78.5 g so we can set up a short equation to calculate the total mass of the soft drink:
We can express 10.5% as a decimal, 0.105.
Total Mass * 0.105=78.5 g
Total Mass=78.5/0.105
Total Mass=747.6 g
The density is given in g/mL, but we want to flip the units around so we can multiply by mass. So, another way to write the density would be 1.04g=1mL or 1ml/1.04g. We can now calculate total volume from total mass:
747.6g*(1mL/1.04g)=718.9 mL
We can double check our math by recalculating the density using the values we found ourselves:
747.6g/718.9 mL=1.04 g/mL
