Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 64 points. They won 11 more games than they tied. How many wins and how many ties did the team have?
64=2W + T
W-11=T
can you take it from there?
To determine the number of wins and ties for the team, we can set up a system of equations based on the given information.
Let's denote the number of wins as W and the number of ties as T.
According to the given information, a team receives 2 points for a win and 1 point for a tie. Therefore, we can express the total number of points obtained by the team as follows:
Total points = 2W + T
Since the team won a championship with 64 points, we have:
2W + T = 64 -- Equation 1
Additionally, it is given that the team won 11 more games than they tied, which can be represented as:
W = T + 11 -- Equation 2
Now we have a system of two equations (Equation 1 and Equation 2) that we can solve simultaneously to find the values of W (wins) and T (ties).
Substituting Equation 2 into Equation 1, we get:
2(T + 11) + T = 64
Simplifying this equation:
2T + 22 + T = 64
Combine like terms:
3T + 22 = 64
Subtracting 22 from both sides:
3T = 42
Dividing both sides by 3:
T = 14
Now that we have found the number of ties (T = 14), we can substitute this value back into Equation 2 to find the number of wins:
W = T + 11
W = 14 + 11
W = 25
Therefore, the team had 25 wins and 14 ties.