3 points for a win and 1 point for a draw. After 23 games Manchester united have 49 points and have lost 4 matches. How many matches have they drawn?I need the answer by tomorrow because the...

3 points for a win and 1 point for a draw. After 23 games Manchester united have 49 points and have lost 4 matches. How many matches have they drawn?

I need the answer by tomorrow because the homework is due tomorrow and also whoever answers it can you please tell me how you worked it out, Thanks.

Asked on by retrokidd

6 Answers | Add Yours

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Total games = 23

game won = x

game drawn = y

Games lost = 4  , Then games won OR draw = 23-4 = 19

Then, x+ y = 19..........(1)

game won = 3 point

game drawn = 1 point

Total points = x*3 + y * 1 = 49

==> 3x + y = 49 .........(2)

Let us use the elemination method.

subtract (1) from (2):

==> 2x = 30

==> x= 15

==> y = 4

Then game won= 15

games drawn = 4

pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

Since they have lost 4 matches (probably Rooney's fault), they have their 49 points from 19 matches.  Therefore, we will need to find out how many wins and draws can come out to 49 points.

We will set up the equations as follows (let the number of wins be W and draws be D)

W + D = 19

3W + D = 49

Now let's use the first equation to get a value for D.

W + D = 19

D = 19 - W

Then we substitute into the second equation.

3W + 19 - W = 49

3W - W = 30

2W = 30

W = 15

This means that they have won 15 matches.  This gave them 45 points.

And therefore they have drawn 4, giving them 4 points for a total of 49.

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

It is known that the team gets 3 points for a win and 1 point for a draw. After 23 games Manchester United has 49 points and the number of matches lost is 4.

As for each loss, there is no deduction of points, the 49 points that Manchester United has are due to matches it has drawn or won.

Let the number of matches drawn be N, the number of matches won is 19 - N.

The total points as a result of this is: 1*N + 3*(19 - N)

= N + 57 - 3N

= -2N + 57

This is equal to 49

-2N + 57 = 49

2N = 8

N = 4

The number of matches drawn is 4

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

Total games played = 23.

games lost = 4.

So  the number of games Manchester United has won or drawn

 = 23- 4= 19. Points ernrned = 49.

We can do this by a common sense :

Had Manchester United drawn all games , then its points wpoud have been 19 only. So  if it win one game, it woud have  decresed the number of draw by 1  and the net increase in the points wpould be 3*1-1*2 = 2.

So it requires manchester to get (49-19) more points to get a total of 49 points and this reqires (49-19)/2 wins = 15 wins.

Therefore Mnchester  united won  15 wins and (19-15) draws = 4, and got points 15*3+4*1 = 49 points.

We can do this by algebra: Let x be the number of winning . then 19-x is the number drawn.

So the number of points won for x wins = 3x and the points earned by the (19-x) draw  is (19-x)*1  = 19-x .

So the total points = 3x+19-x = 49 and solving for x.

 

 

givemoregurie's profile pic

givemoregurie | (Level 1) eNoter

Posted on

This is called a simultaneous equation.

Let the games won be y and the games drawn be x

Total games played y+x+4=23 - You have to add the lost games as they contribute to 23.

Points earned 3y+x=49 - The games won are 3 by y while as the games drawn are 1 by x.

Solving this simultaneously gives:

y+x+4=23 - by elimination y=23-x-4 therefore y=19-x

Substituting y in 3y+x=49 gives 3(19-x)+x=49

57-3x+x=49 therefore -2x=49-57 which is -2x=-8 therefore x=4.

y=23-x-4 thus y=23-4-4 which is y=15.

Therefore Manchester won 15 games drew 4 games and lost 4 games.

Games played=15+4+4=23

Points earned:(3*15)+(1*4)=49 since 3 for win and 1 for a draw.

william1941's profile pic

william1941 | College Teacher | (Level 3) Valedictorian

Posted on

Manchester United has played a total of 23 matches. Of these they have lost 4 matches. According to the information provided, they get 3 points for a win and 1 point for a draw.

As they lost 4 matches, they get no points for these. We have 23-4= 19 matches which have been won or drawn. Let the number of draws be D. So the number of victories is 19-D.

The number of points they get is therefore (19-D)*3+1*D. This is equal to 49.

Solving (19-D)*3+1*D=49, we have:

19*3-3D+D=49

=>2D=57-49=8

=>D=4.

Therefore the number of matches they have drawn is 4.

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