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?
Wins?___
Ties ____
let w = the number of wins
let t = the number of ties.
"Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 64 points."
2w + t = 64
"They won 11 more games than they tied."
w = t+11
To solve this problem, let's set up a system of equations.
Let's assume the number of games the team won is 'W' and the number of games they tied is 'T'.
According to the given information, each win gives 2 points, so the total points from the wins would be 2W. Similarly, each tie gives 1 point, so the total points from the ties would be T. The total points from the entire season is given as 64.
So, we can set up the first equation:
2W + T = 64
The second piece of information states that the team won 11 more games than they tied. Mathematically, this can be written as:
W = T + 11
Now we have a system of two equations:
2W + T = 64
W = T + 11
To solve this system, we can use substitution. We can substitute the second equation (W = T + 11) into the first equation (2W + T = 64):
2(T + 11) + T = 64
2T + 22 + T = 64
3T + 22 = 64
Now, we can solve for T:
3T = 64 - 22
3T = 42
T = 42/3
T = 14
Now that we have the number of ties (T = 14), we can substitute this value back into the second equation to find the number of wins:
W = T + 11
W = 14 + 11
W = 25
Therefore, the team had 25 wins and 14 ties.