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A
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A team begins its season by winning 10 games and losing 14 games. What is the least number of games that the team must play in the remainder of the season so that the team can win at least 5/7 of all of its games in the season?
A) 25
B) 30
C) 35
D) 49
E) 74
Are You Up For the Challenge: 700 Level Questions
A) 25
B) 30
C) 35
D) 49
E) 74
Are You Up For the Challenge: 700 Level Questions
27 Feb 2022, 15:16
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Bunuel
Breaking Down the Info:
Set the number of more games needed to be played as \(x\), and we will need all of these to be wins to find the minimal amount of more games needed.
The new win/loss ratio would be \(10 + x : 14\), which needs to be a 5:2 ratio in order to have a 5:7 win rate.
Then \(\frac{10 + x }{14} = \frac{5}{2}\) and \(x = 25\).
Answer: A
11 May 2023, 22:13
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10 wins + 14 losses = 24 games played in total
The required ratio for wins to total games played is 5/7.
We need to find find the least number of games required to achieve the ratio - let's call this unknown value x.
As we want any game that is played here on out to be a win, we can set up the equation as such:
win / total = 10 + x / 24 + x = 5/7
70 + 7x = 120 + 5x
2x = 50
x = 25
The required ratio for wins to total games played is 5/7.
We need to find find the least number of games required to achieve the ratio - let's call this unknown value x.
As we want any game that is played here on out to be a win, we can set up the equation as such:
win / total = 10 + x / 24 + x = 5/7
70 + 7x = 120 + 5x
2x = 50
x = 25
