The least number of games the team must win to raise its winning record above 75 percent is 18, by raising the win fraction to the total number of fractions as 36/48.
Fractions are ratios representing a part of the whole.
A fraction is written in the form a/b, read as "a by b", and functions a divided by b. a is called the numerator, and b is called the denominator.
To convert a percentage to a fraction, we divide it by 100.
In the question, we are given that a baseball team has won 18 of the 30 games it has played during the season.
We are asked the least number of games the team must win to raise its win record above 75%.
We assume the number of games needed to be x.
The new number of wins will be the sum of current wins and the games to win, that is, the new number of wins = 18 + x.
The new number of games played will be the sum of current games played and the games to win, that is, the new number of games played = 30 + x.
Thus, the win fraction of the team can be shown as the ratio of the total wins to the total number of games played, that is, the win record = (18 + x)/(30 + x).
We are asked to make sure that the win record should be at least 75%,
This percentage can be represented as the fraction 75/100 = 3/4.
Thus, we get the equation:
(18 + x)/(30 + x) = 3/4,
or, 72 + 4x = 90 + 3x,
or, 4x - 3x = 90 - 72,
or, x = 18.
Thus, the least number of games the team must win to raise its winning record above 75 percent is 18, by raising the win fraction to the total number of fractions as 36/48.
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