If he lost x games, then he won (10-x) games. So, you just need to solve
5(10-x)-2x = 22
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?
2 answers
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