Question

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.)

Answer 1

Win:19
Tie:5
(Using algebra will help)

Answer 2

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 = $(12+8+4) = 24$.

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

So sum of total points = $(22+19+14+12) = 67$

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,

$x+y = 24$.......Equation 1

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

$3x+2y = 67$.......Equation 2

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

$y = 24-x$

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

$3x+2(24-x) = 67$

We will expand 2 now.

$3x+48-2x = 67$

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

$3x-2x+48-48 = 67-48$

$3x-2x = 67-48$

$x = 67-48$

$x = 19$

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

The number of games which ended as a tie = $(24-19) = 5$

So we have got the required answers.