Question

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?

Answer 1

If he lost x games, then he won (10-x) games. So, you just need to solve

5(10-x)-2x = 22

Answer 2

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