Batting title math

I find it curious that even though MLB, the player's union and Melky Cabrera agreed that he would not be recognized as batting champion, he is still listed #1 on the MLB stats website (as well as every newspaper listing).

There would be no controversy if the #2 hitter, Buster Posey, wins the title outright. What does he have to do over the last four games of the season?

Cabrera is hitting exactly:
0.34565217391304347826086956521739

(159 hits over 460 at bats (factoring in the one extra at-bat to officially qualify Cabrera for the title)).

Posey is has 175 hits in 520 AB. To better Cabrera's numbers, what minimum number of hits would Posey need?

The formula is:

(175+x)/(520+x) = .3457

Using my basic algebra skills, Posey would need at least 7.52 or 8 hits, ie going 8 for 8. If he does (183/528)= .3466 or .347.

However, that is unlikely. Posey is most likely to get 16-20 more official at bats.

Using this formula: x = .3457 (520 + x)-175

We discovered that 8 for the next 8 is the minimum.

9 AB, he needs 8 hits (rounding up)
10 AB, 9 hits
11 AB, 9 hits
12 AB, 9 hits
13 AB, 10 hits
14 AB, 10 hits
15 AB, 10hits
16 AB, 11 htis
17 AB, 11 hits
18 AB, 11hits
19 AB, 12 hits
20 AB, 12 hits

Not much margin of error.

The exact data, copied from my Excel spreadsheet (note that the at-bats column exceeds the hits column at 8).

# more at bats Hits needed to win 0 1 5.1097 2 5.4554 3 5.8011 4 6.1468 5 6.4925 6 6.8382 7 7.1839 8 7.5296 9 7.8753 10 8.221 11 8.5667 12 8.9124 13 9.2581 14 9.6038 15 9.9495 16 10.2952 17 10.6409 18 10.9866 19 11.3323 20 11.678