The answer to your question appears to be self-evident—the account in Luke is how he would have edited Mark's—because both passages seem to refer to the same incident, although there are a few differences in detail. Jesus is invited to eat in the house of a man named Simon. While he is there, a woman acknowledged to be a sinner appears and uses ointment from an alabaster box to wash Jesus. In each account, Jesus justifies the woman's actions and speaks highly of her.
To account for the discrepancies in the narratives and why Luke would have written and edited Mark's version differently, it's important to remember two things: the two writers have vastly different styles, and neither writer was present when the incident at Simon's house took place. They are both basing their writings on stories that they have heard from eyewitnesses or even from second- or third-hand sources.
Neither of the two writers was one of Jesus's original twelve apostles. Although it's impossible to...
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