At some point in the season, the Unicorns had won 60% of their baseball games. After that point, they won 8 more games and lost 2, to finish the season having won 65% of their games. How many games did the Unicorns play during the season?
After winning 8 games (of 10) their % rose from 60% to 65%. So,
.60n + 8 = .65(n+10)
n = 30
So, they played 40 games altogether.
check:
60% of 30 = 18
18+8=26 is 65% of 40
Let's assume the Unicorns played x games during the season.
We know that at some point in the season, they won 60% of their games, which means they won 0.6x games.
After that point, they won 8 more games and lost 2. So, overall, they won an additional 8 - 2 = 6 games.
The total number of games they won during the season is 0.6x + 6.
According to the information given, this total should be equal to 65% of the total number of games played, which is 0.65x.
Therefore, we can set up the equation:
0.6x + 6 = 0.65x.
To solve this equation, we can subtract 0.6x from both sides:
6 = 0.05x.
Now, divide both sides by 0.05:
x = 120.
Therefore, the Unicorns played 120 games during the season.
To solve this problem, we need to set up a system of equations. Let's assume the total number of games the Unicorns played during the season is 'x'.
First, we know that at some point in the season, they won 60% of their games. So, the number of games they won is 0.6x.
After that point, they won 8 more games and lost 2, which means they won 8 - 2 = 6 games in total. Therefore, the total number of games they won is (0.6x + 6).
Their overall winning percentage for the season is given as 65%. We can translate this to the equation: (0.6x + 6) / x = 65% = 0.65.
To solve this equation, we need to eliminate the percentage by multiplying both sides by 100 to get rid of the decimal, giving us: (0.6x + 6) / x = 0.65.
To simplify the equation, we can remove the fraction by multiplying both sides by x, resulting in: 0.6x + 6 = 0.65x.
Next, we can isolate the variable x by subtracting 0.6x from both sides: 0.6x - 0.65x + 6 = 0.
Simplifying further, we have: -0.05x + 6 = 0.
Now, subtract 6 from both sides to isolate the variable: -0.05x = -6.
Divide both sides by -0.05 to solve for x: x = -6 / -0.05.
Performing the calculation gives us x = 120.
Therefore, the Unicorns played 120 games during the season.
Well, I think I can break it down... I just learned this stuff really really recently, though so excuse me if it's not accurate.
Okay we only know of ten games the unicorns played, right? And only 8 winning were counted from 60% to 65%.
So 8 = 5%
And 13 x 8 = 104
So there were 104 games in which they won. That makes up 65% of the spectrum.
Now we have to find for the games they didn't win which is 35%. If 65% equals 104 what does 35% equal?
I think that's how you'd go about it, but I'm not positive. Sorry, I couldn't finish the equation. I'm exhausted and it's nearly 4 A.M. On the bright side, though you only have one more step to do.