if the yankees scored 965 runs and won 111 of its 162 played games, approximately (to the nearest whole number) how many runs did the team allow their opponent to score?
Please explain thoroughly, thank you for any help!
They scored 965/162 ≈ 6 runs per game
On average, the opponents must have scored 7 runs (or more) in the other 51 games, or at least 357 runs. In the other games, they may have scored anywhere from zero to about 5*51 = 255 runs.
The data is very vague, so if there is some other qualification you intended, maybe you can explain or make the needed adjustments.