Seattle Mariners First-Place Eliminiation Scenario
Seattle must win 13 more games (71 total) to avoid elimination from first place.
Here is a scenario in which Seattle can finish in first place with 71 wins.

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Houston          65	43	54	0.602	0.0
Oakland          61	48	53	0.560	4.5
Seattle          58	51	53	0.532	7.5
Los Angeles      54	54	54	0.500	11.0
Texas            39	69	54	0.361	26.0

Next, we show how the remaining series of games plays out in the scenario:

Houston wins 0 games against Los Angeles and loses 10.
Houston wins 6 games against Oakland and loses 0.
Houston wins 0 games against Seattle and loses 9.
Houston wins 0 games against Texas and loses 7.
Houston wins 0 games agains teams outside the division and loses 0.

Los Angeles wins 10 games against Houston and loses 0.
Los Angeles wins 2 games against Oakland and loses 1.
Los Angeles wins 2 games against Seattle and loses 4.
Los Angeles wins 3 games against Texas and loses 5.
Los Angeles wins 0 games agains teams outside the division and loses 0.

Oakland wins 0 games against Houston and loses 6.
Oakland wins 1 games against Los Angeles and loses 2.
Oakland wins 9 games against Seattle and loses 0.
Oakland wins 0 games against Texas and loses 9.
Oakland wins 0 games agains teams outside the division and loses 0.

Seattle wins 9 games against Houston and loses 0.
Seattle wins 4 games against Los Angeles and loses 2.
Seattle wins 0 games against Oakland and loses 9.
Seattle wins 0 games against Texas and loses 6.
Seattle wins 0 games agains teams outside the division and loses 0.

Texas wins 7 games against Houston and loses 0.
Texas wins 5 games against Los Angeles and loses 3.
Texas wins 9 games against Oakland and loses 0.
Texas wins 6 games against Seattle and loses 0.
Texas wins 0 games agains teams outside the division and loses 0.

Combining the current standings with the wins and losses from the scenario results in the following final standings:
Team             W	L	PCT	GB
Seattle          71	91	0.438	0.0
Houston          71	91	0.438	0.0
Los Angeles      71	91	0.438	0.0
Oakland          71	91	0.438	0.0
Texas            66	96	0.407	5.0


Next, we explain why Seattle cannot win the division with fewer than 71 wins.

There are a total of 43 games left in the following series of games between teams in the American League West:
Houston          vs. Los Angeles      10 games
Houston          vs. Oakland          6 games
Houston          vs. Seattle          9 games
Los Angeles      vs. Oakland          3 games
Los Angeles      vs. Seattle          6 games
Oakland          vs. Seattle          9 games

For each team listed above, the table below shows the current number of wins in the (W) column.
The next column shows the maximum number of its remaining games that each team can win assuming that
Seattle finishes in first place with a total of 70 wins.

Team             W	Max Additional Wins
Houston          65	70 - 65 = 5
Los Angeles      54	70 - 54 = 16
Oakland          61	70 - 61 = 9
Seattle          58	70 - 58 = 12
Total            238	42

Since the total of the Max Additional Wins column is less than 43, it is not possible for Seattle to win the division with 70 (or fewer) total wins.