# Solve this mole fraction calculation with incomplete information

I am currently trying to solve a problem that seems quite simple at the beginning but the complexity reveals itself soon thereafter. The problem is the following:

You mix a known mass of water with a known mass of ethanol. Then you fill up the flask to the 50 mL mark with water, but cannot weigh the contents when you're done. What is the molar fraction of ethanol in this mixture?

My attempt at solving this problem is to basically calculate the initial molar fraction, and then stepwise add small virtual amounts of water. Then the new molar fraction is calculated, and somehow the excess volume (which is negative for the water-ethanol mixture) would also be included somewhere here. This is repeated until the final volume is reached.

An other attempt would be to simply neglect the excess volume. While this might be fine at the edges of the molar fractions, it would introduce a grave error towards the middle. Or is the error still negligible?

Are these reasonable attempts or am I completely missing something here?