Can you please explain this in detail so I can write it down and know how to do it for future reference?
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 they have?
number of games tied: x
number of games won : x+11
2(x+11) + x = 64
solve
W=L+11
2W+1*L=64
Now, put L+11 in for W on the bottom equation.
2(L+11)+L=64
solve for L
Thank you guys
Certainly! Let's break down the problem step by step and solve it.
Step 1: Understand the problem.
We are given that a hockey team won a championship with 64 points. Each win earns them 2 points and each tie earns them 1 point. We're also told that the team won 11 more games than they tied. We need to find the number of wins and ties.
Step 2: Assign variables.
Let's use "W" to represent the number of wins and "T" to represent the number of ties.
Step 3: Set up equations.
Since each win earns 2 points and each tie earns 1 point, we can create an equation for the total number of points.
Total Points = (Number of Wins x 2) + (Number of Ties x 1)
64 = (2W) + (T)
We're also given that the team won 11 more games than they tied. We can express this as:
Number of Wins = Number of Ties + 11
Step 4: Substitute equations.
We can substitute the equation for the number of wins into the equation for total points.
64 = (2(T+11)) + (T)
Step 5: Simplify and solve the equation.
Distribute the 2 into the parentheses.
64 = 2T + 22 + T
Combine like terms.
64 = 3T + 22
Subtract 22 from both sides.
64 - 22 = 3T
42 = 3T
Divide by 3 to solve for T.
T = 42 / 3
T = 14
Step 6: Find the number of wins.
Since the number of wins is 11 more than the number of ties, we can find it by adding 11 to the number of ties.
W = T + 11
W = 14 + 11
W = 25
Step 7: Verify the solution.
We can verify the solution by substituting the values of W and T into the equation for total points.
64 = (2W) + (T)
64 = (2 * 25) + 14
64 = 50 + 14
64 = 64
Step 8: Answer the question.
Therefore, the team had 25 wins and 14 ties.
Now you can write down the solution and the steps for future reference.