In a four-team basketball league, each team has played every other team 4 times. a team earned 3 points for a win, 1 point for a tie and no points for a loss. the total accumulated points were: bulls 22, lakers 19, knicks 14 and warriors 12. how many games ended in a win and how many games ended in a tie? (hint: you might want to start by figuring out how many games total were played, how many points were available, and the combinations of how the teams received the points.)

Here, 4 teams given. Each teams has played every other teams 4 times.

So to find total number of games, we know that Bulls played with the other 3 teams by 4 times that is (4×3) = 12, Lakers played with the other two teams by 4 times that is (4×2) = 8, Knicks played with Warriors 4 times.

Therefore, total number of games = .

Total points given, for Bulls = 22, for Lakers = 19, for Knickers = 14, for Warriors = 12.

So sum of total points =

For a win a team earned 3 points and for a tie two teams win 1 point.

That means for tie total point = 1+1 = 2.

Let's take total number of game which ended as win played be x and total number of game which ended as a tie be y.

We have got total number of games is 24.

So we can write the equations as,

.......Equation 1

And also we have got total number of points is 67. So the equation is,

.......Equation 2

From equation 1, if we move x to the right side we will get,

Now let's substitute this value in equation 2, to get the value of x. By substituting the value we will get,

We will expand 2 now.

We will move 48 to the other side by subtracting it from both sides. We will get,

So the number of games which ended as a win = 19

The number of games which ended as a tie =

So we have got the required answers.

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