A team has won 60 percent of the games it has played so far. If the team wins the 15 remaining games in the season, it will have won 80 percent of the season's games. How many games will the team play over the entire season?
60 % = 60 / 100 = 0.6
80 % = 80 / 100 = 0.8
x = Number of games in season
A team has played so far x - 15 games and won 60 % of the games .
So :
0.6 * ( x - 15 ) + 15 = 0.8 x
0.6 x - 0.6 * 15 + 15 = 0.8 x
0.6 x - 9 + 15 = 0.8 x
0.6 x + 6 = 0.8 x Subtract 0.6 x to both sides
0.6 x - 0.6 x+ 6 = 0.8 x - 0.6 x
6 = 0.2 x Divide both sides by 0.2
6 / 0.2 = 0.2 x / 0.2
30 = x
x = 30
Proof :
A team has played so far x - 15 = 30 - 15 = 15 games
A team has won 0.6 * 15 = 9 games
If the team wins the 15 remaining games in the season, it will have 9 + 15 = 24 won games
24 / 30 = 0.8 = 0.8 * 100 / 100 = 80 / 100 = 80 %
To find out how many games the team will play over the entire season, we need to determine the total number of games played so far and the number of games remaining in the season.
Let's start by finding the total number of games played so far. We know that the team has won 60 percent of its games, which means it has lost the remaining 40 percent. Since the winning percentage is given in relation to the total number of games played, we can express the winning percentage as a fraction. Thus, the team has won 60/100 or 3/5 of its games.
Let's assume the team has played x number of games so far. According to the information given, the team has won 3/5 of x games. This can be written as (3/5)x.
Therefore, the number of games the team has lost so far is represented by the remaining fraction, which is (2/5)x.
Next, we can determine the number of games the team has won out of the total number of games played so far and the remaining 15 games. Since the team will have won 80 percent of the season's games after winning the remaining 15 games, we can express this as a fraction. Thus, the team will have won 80/100 or 4/5 of the total number of games played in the season.
Considering the total number of games played so far and the remaining 15 games, the team will have won (3/5)x + 15 games in total.
Therefore, (3/5)x + 15 represents the number of games the team has won out of the total number of games played so far and the remaining games. This number should also equal to 4/5 of the total number of games played in the season.
Now, we can set up an equation to find the value of x:
(3/5)x + 15 = (4/5)(x + 15)
To solve this equation, we can start by multiplying both sides by 5 to eliminate the denominators:
5[(3/5)x + 15] = 5[(4/5)(x + 15)]
This simplifies to:
3x + 75 = 4(x + 15)
Expanding on the right side:
3x + 75 = 4x + 60
Now, we can solve for x:
Subtracting 3x from both sides:
75 = x + 60
Subtracting 60 from both sides:
15 = x
Therefore, the team has already played 15 games so far.
To find the total number of games the team will play over the entire season, we need to add the number of games played so far to the remaining 15 games:
Total number of games = Number of games played so far + Remaining games
Total number of games = 15 + 15
Total number of games = 30
Hence, the team will play 30 games over the entire season.