hockey teams receive 2 points whey they win and 1 point whey they tie. one season, a team won a championship with 51 points. they won 9 more games than they tied. how many wins and how many ties did the team have?
how many wins did the team have?____
how many ties did the team have?_____
I don't believe in answering question from students that begin sentences with a lower case letter. However, I'll help this time. A word to the wise?
Let w = wins
and t = ties
w+t=51
w=t+9
Two equations and two unknowns. Solve for w and t.
To determine the number of wins and ties for the hockey team, we can set up a system of equations based on the given information.
Let's assume the number of wins is represented by "W" and the number of ties is represented by "T."
According to the given information:
1) Each win is worth 2 points, so the total points from wins would be 2W.
2) Each tie is worth 1 point, so the total points from ties would be 1T.
3) The team won a total of 51 points, so the equation would be: 2W + 1T = 51.
4) The team won 9 more games than they tied, so the equation would be: W = T + 9.
To solve this system of equations, we can substitute the second equation into the first equation:
2(T + 9) + T = 51
2T + 18 + T = 51
3T + 18 = 51
3T = 51 - 18
3T = 33
T = 33 / 3
T = 11
Now that we have the number of ties, we can substitute this value back into the second equation to find the number of wins:
W = T + 9
W = 11 + 9
W = 20
Therefore, the team had 20 wins and 11 ties.