Hockey Teams Receive 2 Points When They Win And 1 Point When They Tie. One Season A Team Won A Championship With 65 Point. They Won 10 More Games Than They Tied. How Many Wins And How Many Ties Did The Team Have?
Let's assume the number of games the team tied is x.
The team won 10 more games than they tied, so the number of wins is x + 10.
Since each win is worth 2 points and each tie is worth 1 point, the total number of points can be calculated as follows:
Total points = (number of wins * 2) + (number of ties * 1)
Given that the team won the championship with 65 points, we can write this equation:
65 = (x + 10) * 2 + x * 1
Simplifying this equation, we get:
65 = 2x + 20 + x
Combining like terms, we have:
65 = 3x + 20
Subtracting 20 from both sides of the equation, we get:
45 = 3x
Dividing both sides by 3, we find:
x = 15
Now we can substitute the value of x back into one of the previous equations to find the number of wins:
Number of wins = x + 10 = 15 + 10 = 25
Therefore, the team had 25 wins and 15 ties in the season.
Let's solve this problem step by step.
First, let's assume that the team won "x" games and tied "y" games.
According to the given information, the team won 10 more games than they tied. Therefore, we can write the equation:
x = y + 10
Next, we know that a win earns 2 points, and a tie earns 1 point. So, we can calculate the total points earned by the team:
Total Points = (2 * number of wins) + (1 * number of ties)
Given that the team won a championship with 65 points, we can write the equation:
65 = (2 * x) + (1 * y)
Now we can substitute the value of "x" from the first equation into the second equation:
65 = (2 * (y + 10)) + (1 * y)
Simplifying the equation:
65 = 2y + 20 + y
Combine like terms:
65 = 3y + 20
Subtract 20 from both sides of the equation:
65 - 20 = 3y
45 = 3y
Divide both sides of the equation by 3:
45/3 = y
y = 15
Now substitute the value of "y" into the first equation to find the value of "x":
x = 15 + 10
x = 25
Therefore, the team won 25 games and tied 15 games.