I am having problems with both of these questions.
1. Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 67 points. They won 11 more games than they tied. How many wins and ties did the team have?
Wins?
Ties?
2*w+1*T=67
w-T=11
Ties=15
Wins=26
2w+1t=67
w=t+11
Use substitution method
To solve this problem, let's assign some variables:
Let W be the number of wins.
Let T be the number of ties.
According to the given information, we know that each win contributes 2 points, and each tie contributes 1 point. The team won a championship with 67 points, so we can write an equation based on the points:
2W + 1T = 67
We also know that the team won 11 more games than they tied. Mathematically, we can write this as:
W = T + 11
Now we have a system of two equations with two variables. We can solve them simultaneously to find the values of W and T.
Substitute the value of W from the second equation into the first equation:
2(T + 11) + 1T = 67
Simplify:
2T + 22 + 1T = 67
3T + 22 = 67
Subtract 22 from both sides:
3T = 67 - 22
3T = 45
Divide both sides by 3:
T = 45 / 3
T = 15
Now we know the number of ties, which is 15. Substitute this value back into the second equation to find the number of wins:
W = 15 + 11
W = 26
Therefore, the team had 26 wins and 15 ties.