In a four-team basketball league, each team has played every other team 4 times. a team earned 3 points for a win, 1 point for a tie and no points for a loss. the total accumulated points were: bulls 22, lakers 19, knicks 14 and warriors 12. how many games ended in a win and how many games ended in a tie?

Ok so heres how to approach this. If a game ends in a win, 3 total points are awarded. 3 to the winner, 0 to the loser. If a game ends in a tie, 2 points are awarded total, one to each team. The total points awarded is 22+19+14+12=67. Because there are 4 teams, there are 2 games per week (2 teams per game) and 12 weeks so 24 total games. So if t=games tied and w=games ended in a win, we have 2 equations. 3w+2t=67 and t+w=24. Solving for t, t=24-w. Plugging into the other equation, 3w+2(24-w)=67. Which is w+48=67 so w=19 and t+19=24 so t=5.

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