SOLUTION: Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 57 points. They won 9 more games than they tied. How many wins

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Question 146202: Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 57 points. They won 9 more games than they tied. How many wins and how many ties did the team have?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let w=# of wins, and t=# of ties


The sentences "Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 57 point" translate to the first equation 2w%2Bt=57

And the sentence "They won 9 more games than they tied" translates to the second equation w=t%2B9




Start with the given system
2w%2Bt=57
w=t%2B9



2%28t%2B9%29%2Bt=57 Plug in w=t%2B9 into the first equation. In other words, replace each w with t%2B9. Notice we've eliminated the w variables. So we now have a simple equation with one unknown.


2t%2B18%2Bt=57 Distribute


3t%2B18=57 Combine like terms on the left side


3t=57-18Subtract 18 from both sides


3t=39 Combine like terms on the right side


t=%2839%29%2F%283%29 Divide both sides by 3 to isolate t



t=13 Divide




Now that we know that t=13, we can plug this into w=t%2B9 to find w



w=%2813%29%2B9 Substitute 13 for each t


w=22 Simplify


So our answer is w=22 and t=13 which means that the team won 22 games and tied 13 games