Asked by solomon
                In a competition 5 points are awarded for each game won and 2 points deducted for game lost.A boy took place in the competition and got 22 points after taking part in 10 games.how many games did he lose?
            
            
        Answers
                    Answered by
            oobleck
            
    If he lost x games, then he won (10-x) games. So, you just need to solve
5(10-x)-2x = 22
    
5(10-x)-2x = 22
                    Answered by
            Bosnian
            
    N = number of games played = 10
W = number of games won
L = number of lost games
If he played 10 games and won the W games, he lost 10 - W games.
This means:
L = 10 - W
5 points are awarded for each game won
2 points deducted for game lost
Total number of points = 22
This means:
W ∙ 5 - L ∙ 2 = 22
5 W - 2 L = 22
Replace L = 10 - W in this equation.
5 W - 2 ( 10 - W ) = 22
5 W - 2 ∙ 10 - 2 ∙ ( - W ) = 22
5 W - 20 + 2 W = 22
7 W - 20 = 22
Add 20 to both sides
7 W - 20 + 20 = 22 + 20
7 W = 42
Divide both sides by 7
W = 6
He won 6 games.
L = 10 - W = 10 - 6 = 4
He lose 4 games.
Proof:
Total number of points = 5 W - 2 L = 5 ∙ 6 - 2 ∙ 4 = 30 - 8 = 22
    
W = number of games won
L = number of lost games
If he played 10 games and won the W games, he lost 10 - W games.
This means:
L = 10 - W
5 points are awarded for each game won
2 points deducted for game lost
Total number of points = 22
This means:
W ∙ 5 - L ∙ 2 = 22
5 W - 2 L = 22
Replace L = 10 - W in this equation.
5 W - 2 ( 10 - W ) = 22
5 W - 2 ∙ 10 - 2 ∙ ( - W ) = 22
5 W - 20 + 2 W = 22
7 W - 20 = 22
Add 20 to both sides
7 W - 20 + 20 = 22 + 20
7 W = 42
Divide both sides by 7
W = 6
He won 6 games.
L = 10 - W = 10 - 6 = 4
He lose 4 games.
Proof:
Total number of points = 5 W - 2 L = 5 ∙ 6 - 2 ∙ 4 = 30 - 8 = 22
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