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?
If he lost x games, then he won (10-x) games. So, you just need to solve
5(10-x)-2x = 22
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
Let's assume the number of games the boy won as "x" and the number of games he lost as "y".
According to the given information:
5 points are awarded for each game won, so the total points for the games won is 5x.
2 points are deducted for each game lost, so the total points deducted for the games lost is 2y.
The total points the boy got after taking part in 10 games is 22. Therefore, we have the equation:
5x - 2y = 22. [Equation 1]
We also know that the boy took part in a total of 10 games. So, we have another equation:
x + y = 10. [Equation 2]
To solve the system of equations, we can use the substitution method.
From equation 2, we have:
x = 10 - y.
Substituting this value of x in equation 1, we get:
5(10 - y) - 2y = 22.
Expanding this equation, we get:
50 - 5y - 2y = 22.
Combining like terms, we have:
50 - 7y = 22.
Simplifying further, we get:
-7y = 22 - 50,
-7y = -28.
Dividing both sides of the equation by -7, we get:
y = 4.
Therefore, the boy lost 4 games.
To find out how many games the boy lost, we can set up a system of equations based on the information given.
Let's assume the boy won x games and lost y games.
According to the problem, 5 points are awarded for each game won and 2 points deducted for each game lost. The boy got 22 points in total after taking part in 10 games.
So, we can set up the following equations:
1) x + y = 10 (total games played)
2) 5x - 2y = 22 (total points earned)
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution to solve these equations:
From equation 1, we have x = 10 - y.
Substituting this value of x into equation 2, we get:
5(10 - y) - 2y = 22.
Simplifying the equation, we have:
50 - 5y - 2y = 22,
-7y = -28,
y = 4.
Therefore, the boy lost 4 games.