+197 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.
+592 3x+y=70
x+y=38
subtract equation 2 from equation 1:
2x=32
x=16
16+y=38
y=$\boxed{22}$
+318 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.
+129852 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
