In a competition 3 points were awarded for each game won and 2 points were deducted for each game lost a pupil attempted 5 games and got 5 points how many games did he lose
Let the no of games that he lost be x
no of games won= 5-x
points awarded= 3(5-x)= 15-3x
points deducted= 2x
15-3x+2x=5
15-x=5
-x=5-15
-x=-10
x=10
therefore, he lost 10 games
Sorry, I have done your question wrongly. Avoid the above workings and follow this new workings.
METHOD 1
Let the number of games lost be x
games won=5-x
points awarded= 3(5-x)=15-3x
points deducted= 2x
points deducted must be subtracted from points awarded to get the required points
15-3x-2x=5
15-5x=5
-5x=5-15
-5x=-10
x=2
therefore, he lost 2 games
METHOD 2
Let the number of games won be x and those lost be y
x+y=5....eqn(i)
points awarded= 3x
points deducted= 2y
subtract 2y from 3x
3x-2y=5....eqn(ii)
from eqn(i) x=5-y
substitute x=5-y in eqn(ii)
3(5-y)-2y=5
15-3y-2y=5
15-5y=5
-5y=5-15
-5y=-10
y=2
therefore, he lost 2 games