John,Paige and kaylee go bowling.John has played 3 times as many as kaylee.Paige has played 6 more games than kaylee.John has played 6 more games than Paige.How many games has Paige played?
Let the number of games Kaylee has played be x.
John has played 3 times as many games as Kaylee, so he has played 3x games.
Paige has played 6 more games than Kaylee, so she has played x+6 games.
John has played 6 more games than Paige, so he has played (x+6)+6 = x+12 games.
Since John has played 3 times as many games as Kaylee, and he has played x+12 games, we can equate them to get 3x = x+12.
Subtracting x from both sides, we get 2x = 12.
Dividing both sides by 2, we get x = 6.
So Kaylee has played 6 games.
Paige has played x+6 = 6+6 = 12 games. Answer: \boxed{12}.
Let's first assign variables to each person's number of games played:
Let K be the number of games played by Kaylee.
Since John has played 3 times as many as Kaylee, John has played 3K games.
And since Paige has played 6 more games than Kaylee, Paige has played K + 6 games.
Additionally, John has played 6 more games than Paige, so John has played K + 6 + 6 = K + 12 games.
Now we can set up an equation using the given information:
John's games + Paige's games + Kaylee's games = Total games played
(3K) + (K + 6) + K = Total games played
Combining like terms:
3K + K + 6 + K = Total games played
5K + 6 = Total games played
Since John, Paige, and Kaylee are the only ones who played, the total games played should be the sum of their individual numbers of games played.
5K + 6 = K + 6 + K + K
Simplifying further:
5K + 6 = 3K + 6
Subtracting 3K from both sides:
5K - 3K + 6 = 3K - 3K + 6
2K + 6 = 6
Subtracting 6 from both sides:
2K + 6 - 6 = 6 - 6
2K = 0
Dividing both sides by 2:
2K/2 = 0/2
K = 0
Now that we know Kaylee played 0 games, we can substitute this value back into our equation to find Paige's number of games played:
Paige's games = Kaylee's games + 6 = 0 + 6 = 6
Therefore, Paige has played 6 games.