The Rockets and the Rangers are in a league where each of the teams plays $100$ games. At some point in the season, the Rockets' ratio of their wins to their losses is $3:2,$ the Rangers' ratio of their wins to their losses is $7:13,$ and both teams have the same number of games left to play. If the Rockets lose all of their remaining games while the Rangers win all of their remaining games, the teams will end the season with the same number of wins. At this point in the season, how many games do the Rockets have left to play?