+0  
 
+1
33
3
avatar+91 

A football team played 38 games in a tournament and collected a total of 70 points. 3 points were awarded for a win and 1 point for games they tied. No points were deducted for games they lost. The team won twice as many games as they tied. Find the number of games the team lost.

 Apr 20, 2021
 #1
avatar+496 
-1

3x+y=70
x+y=38

subtract equation 2 from equation 1:

2x=32
x=16

16+y=38

y=$\boxed{22}$

 Apr 20, 2021
edited by SparklingWater2  Apr 20, 2021
 #2
avatar+119 
+3

1 group --> 2 wins + 1 draw 

Points for a group of 2 wins and 1 draw

--> 2 * 3 + 1 * 1

= 7

No points were scored for any loses, so all the 70 points must be due to the wins and draws, which were in groups of 2 wins and 1 draw.

70 ÷ 7 = 10 (Number of groups)

3 * 10 = 30 (Total wins and draws)

38 - 30 = 8

The team lost 8 games.

 Apr 20, 2021
 #3
avatar+118505 
+2

Let the  number of  games  tied  =  T

Let  the number of  games  won  =  2T

 

So

 

Games won * points  for  each win  =  Games tied *  points for  each tie  =  total  points

 

So

 

(2T)(3)  + T(1)  =  70

 

6T  + T   = 70

 

7T  = 70

 

T = 70 / 7   =   10  =  games tied

 

2T  = 20  = games won

 

So

 

38  -  10  - 20  =  8  = games  lost

 

cool cool cool

 Apr 20, 2021

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