Given that the team played 147 and the ratio of games won to games lost is 4:3, that means that for every four games they won, they lost three.
For these problems, it is often easier to rewrite the ratio as a fraction, so 4:3 as 4/7. (These are equivalent because the first ratio is four in a sample of four plus three, or four out of seven.)
So, we can write
.
Therefore, the team won 84 games.