In june a baseball team that played 60 games had won 30% of its game played. After a phenomenal winning streak this team raised its average to 50% .How many games must the team have won in a row to attain this average?
12
20
24
30
After 60 games at 30%, the team won 18 games. To reach 50% overall, let x be additional wins needed: (18+x)/(60+x) = 0.5. Solving: 18+x = 30+0.5x, so 0.5x = 12, x = 24. They must win 24 consecutive games.
To solve this problem, we can set up an equation to represent the given information.
Let's assume that the team won "x" games in a row to attain an average of 50%.
In June, the team played 60 games and won 30% of them. This means they won 0.3 * 60 = 18 games.
After the winning streak, the team won x games in a row. So, the total number of games won is 18 + x.
The average winning percentage is given by the equation:
[ \text{Average winning percentage} = \frac{\text{Total number of games won}}{\text{Total number of games played}} ]
We can now set up the equation:
[ \frac{18 + x}{60 + x} = 0.5 ]
To solve for x, we can cross-multiply and solve the resulting equation:
[ 18 + x = 0.5(60 + x) ]
Simplifying the equation:
[ 18 + x = 30 + 0.5x ] [ 0.5x - x = 30 - 18 ] [ -0.5x = 12 ] [ x = \frac{12}{-0.5} ] [ x = -24 ]
Since it doesn't make sense to have a negative number of games won in a row, we can ignore the negative sign and take the absolute value of x:
[ |x| = 24 ]
Therefore, the team must have won 24 games in a row to attain an average of 50%.
The correct answer is C) 24.