the senior girls volleyball team has won 70% of the 30 games it has played. the number of the remaining 14 games that the team must win in order to have a 75% for the season is...
a) 2 b) 5 c) 10 d) 11 e) 12
To find the solution, we can use the concept of percentages and proportions.
We know that the senior girls volleyball team won 70% of the 30 games it has played. This means they won 70% of 30, which is (70/100) * 30 = 21 games.
Now, let's assume that the team wins 'x' out of the remaining 14 games. According to the question, they need to have a 75% win rate for the entire season.
To calculate the total number of games:
Total games played = Games won + Games remaining
Total games played = 21 + x
The team's win rate for the entire season is given by:
Win rate = (Total games won / Total games played) * 100
As per the question, the win rate for the entire season should be 75%:
75 = (Games won / (Games won + Games remaining)) * 100
Let's solve for 'x' to find out how many games the team needs to win out of the remaining 14 games:
75 = (21 / (21 + x)) * 100
Divide both sides by 100:
0.75 = 21 / (21 + x)
Cross multiply:
0.75 * (21 + x) = 21
15.75 + 0.75x = 21
Subtract 15.75 from both sides:
0.75x = 5.25
Divide both sides by 0.75:
x = 7
Therefore, the team needs to win 7 out of the remaining 14 games to have a win rate of 75% for the season.
However, none of the given answer choices ('a', 'b', 'c', 'd', 'e') match the calculated result of 7. Please double-check the answer choices provided.