Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 53 points. They won 10 more games than they tied. How many wins and how many ties did the team have? How many wins did the team have?

Breakdown

Let's assume that the number of ties the team had is "x".

According to the given information, the team had 10 more wins than ties. So, the number of wins the team had would be "x + 10".

Now, let's calculate the total points:

The team received 2 points for each win, so the total points from wins would be 2*(x + 10).

The team received 1 point for each tie, so the total points from ties would be 1*x.

The total points of the team, based on the given championship win, are 53.

Therefore, we can set up the equation:

total points from wins + total points from ties = 53

2*(x + 10) + 1*x = 53

Simplifying the equation:

2x + 20 + x = 53

3x + 20 = 53

3x = 53 - 20

3x = 33

x = 33/3

x = 11

So, the team had 11 ties.

Now, let's calculate the number of wins:

Number of wins = Number of ties + 10

Number of wins = 11 + 10

Number of wins = 21

Therefore, the team had 21 wins and 11 ties.

To determine the number of wins and ties the team had, let's denote the number of wins as "W" and the number of ties as "T".

We know that a win is worth 2 points, and a tie is worth 1 point. The team won a total of 53 points for the season. Therefore, we can set up the following equation:

2W + 1T = 53

We are also given that the team won 10 more games than they tied. In equation form, this is:

W = T + 10

Now we have a system of two equations with two variables:

2W + T = 53 (Equation 1)
W = T + 10 (Equation 2)

To solve this system, we can substitute Equation 2 into Equation 1:

2(T + 10) + T = 53

Simplifying this equation, we get:

2T + 20 + T = 53
3T + 20 = 53
3T = 33
T = 11

Now we can substitute the value of T back into Equation 2 to find W:

W = 11 + 10
W = 21

Therefore, the team had 21 wins and 11 ties.

In conclusion, the team had 21 wins and 11 ties.

53=2W+T

W=10+T

Does that help?