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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? (Hint: you might want to start by figuring out how many games total were played, how many points were available, and the combinations of how the teams received the points.)

Respuesta :

mathmate
Given:
four teams
each team plays every other team four times
3+0=3 points for a win in a match
1+1=2 points for a tie in a match
total number of points = 22+19+14+12=22+33+12=55+12=67 points

Total number of games played = (4*3/2)*4=24
Maximum number of points =24*3=72
For each tied match, there will be 3-2=one point less in the total.
Therefore there were 72-67=5 tied games, and 24-5=19 games won.

Total 19*3+5*2=57+10=67 points.  ok.

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