Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 61 points. They won 11 more games than they tied. How many wins and how many ties did the team have?
X Ties and (X+11) Wins.
1*X + 2(X+11) = 61 Points.
X + 2X + 22 = 61
3X = 61 -22 = 39
X = 13 Ties.
X + 11 = 13 + 11 =24 Wins.
To determine the number of wins and ties, 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, each win is worth 2 points, so the team's total points from wins can be calculated as 2W.
Each tie is worth 1 point, so the team's total points from ties can be calculated as 1T.
The total points accumulated by the team can be expressed as the sum of points from wins and points from ties:
2W + 1T = 61 (equation 1)
We are also given that the number of wins is 11 more than the number of ties:
W = T + 11 (equation 2)
Now we can solve this system of equations to find the values of W (wins) and T (ties).
Using equation 2, we can substitute (T+11) for W in equation 1:
2(T+11) + 1T = 61
Simplifying, we get:
2T + 22 + 1T = 61
Combining like terms:
3T + 22 = 61
Subtracting 22 from both sides:
3T = 39
Dividing both sides by 3:
T = 13
Now that we have the value of T, we can substitute it back into equation 2 to find the value of W:
W = T + 11 = 13 + 11 = 24
Therefore, the team had 24 wins and 13 ties.