In a competition ,5 points were awarded for each game won and 2 points for each game were deducted for each game lost .A pupil attempted 15 games and got 54 points .How many games did the pupil win?
x=wins
y=losses
x+y = 15
5x-2y = 54
so, substituting for y,
5x-2(15-x) = 54
x=12
In a competition 5 points is awarded for each game won while 3 points is deducted for each game lost. A school participated in 20 games and won 14.how many points did it lose?
Well, it looks like we have a mathematical puzzler here! Let's do some clown-like calculations to figure it out.
Let's assume the pupil won "w" games out of the 15 games attempted. Since 5 points are awarded for each game won, the total points earned from the wins would be 5w.
Now, for each game lost, 2 points are deducted. So, the total points deducted would be 2 times the number of games lost, which is (15 - w).
Adding up the points earned and points deducted, we get the total points of 54:
5w - 2(15 - w) = 54
Simplifying the equation, we have:
5w - 30 + 2w = 54
Combining like terms:
7w - 30 = 54
Now, let's bring the numbers to one side:
7w = 54 + 30
7w = 84
And finally, let's solve for w, the number of games won:
w = 84 / 7
w = 12
So, the pupil won 12 games out of the 15 attempted. Way to go, pupil! That's some impressive game-playing skills!
Let's assume the pupil won x games.
According to the given information, the pupil lost (15 - x) games.
For each game won, 5 points are awarded, so the total points gained from winning games is 5x.
For each game lost, 2 points are deducted, so the total points deducted from losing games is 2(15 - x).
Thus, the total points the pupil got can be calculated by subtracting the points deducted from the points gained:
Total points = Points gained - Points deducted
54 = 5x - 2(15 - x)
Simplifying the equation:
54 = 5x - 30 + 2x
54 = 7x - 30
84 = 7x
x = 12
Therefore, the pupil won 12 games.
To find out how many games the pupil won, we can set up a system of equations based on the given information.
Let's assume that the number of games the pupil won is represented by W, and the number of games the pupil lost is represented by L.
According to the given information, the pupil attempted 15 games in total. Therefore,
W + L = 15 (Equation 1)
The pupil was awarded 5 points for each game won, and 2 points were deducted for each game lost. So the total number of points the pupil earned can be expressed as:
5W - 2L = 54 (Equation 2)
Now we can solve this system of equations to find the values of W (the number of games won) and L (the number of games lost).
From Equation 1, we can rewrite it as W = 15 - L.
Substituting this expression into Equation 2, we get:
5(15 - L) - 2L = 54
75 - 5L - 2L = 54
75 - 7L = 54
Simplifying further:
-7L = 54 - 75
-7L = -21
Dividing both sides by -7:
L = -21 / -7
L = 3
Substituting this value in Equation 1:
W + 3 = 15
W = 15 - 3
W = 12
Therefore, the pupil won 12 games.