Adam and Eve – Who Started It?

Here’s a problem for you: Genesis is very clear about the order of events in the story we all know: The serpent tempts Eve, Eve succumbs, Adam then fails to put his foot down with his wife and both are thrown out of Eden.

But I’ve thought of a problem: if Adam had stepped up instead of taking the apple from Eve, then how would it have made any difference? I mean, how could one be in Eden and not the other? Didn’t she seal both of their fates the moment she ate?