Define a variable and write an inequality. Then solve. So far, they have won 9 games and lost 2. How many more games must they win this season to win at least 75% of all their games?
I will be glad to critique your thoughts on this one. Let X be the number of games they must win. You will need to know the number of games in a saeason. That depends upon the sport. in ML baeball, it is 162.
To solve this question, let's define the variable as the total number of games they need to win this season.
Let x be the total number of games they need to win this season.
The inequality we can write is:
(9 + x) / (9 + x + 2) ≥ 75/100
Now, let's solve for x:
Expanding the equation, we have:
(9 + x) / (11 + x) ≥ 75/100
Cross multiplying, we get:
100(9 + x) ≥ 75(11 + x)
Distributing, we have:
900 + 100x ≥ 825 + 75x
Combining like terms, we get:
100x - 75x ≥ 825 - 900
Simplifying further,
25x ≥ -75
Dividing both sides by 25, we have:
x ≥ -3
Since the number of games cannot be negative, it means they need to win at least 3 more games this season to win at least 75% of all their games.
To solve this problem, we need to define a variable and write an inequality based on the given information.
Let's say the number of games they need to win is represented by the variable 'x'.
We can write an inequality based on the given information that the number of games won should be at least 75% of all their games. In mathematical terms, this can be written as:
(9 + x)/(9 + x + 2) ≥ 0.75
Here, the numerator represents the number of games won (9 + x) and the denominator represents the total number of games played (9 + x + 2, where 2 represents the number of games lost).
Now, let's solve the inequality to find out how many more games they must win this season.
(9 + x)/(11 + x) ≥ 0.75
Multiplying both sides by (11 + x) to eliminate the denominator:
(9 + x) ≥ 0.75(11 + x)
Expanding and simplifying:
9 + x ≥ 8.25 + 0.75x
Subtracting 0.75x from both sides:
9 - 0.75x + x ≥ 8.25
Combining like terms:
1.25x ≥ -0.75
Dividing both sides by 1.25:
x ≥ -0.75/1.25
Simplifying:
x ≥ -0.6
Since the number of games must be a whole number, we can conclude that they must win at least 1 more game this season to win at least 75% of all their games.