GPA 4.0を取るための公式

3.2を取ってしまった学生が挽回して3.9を取るためには何個A(=4.0)を取る必要があるかの公式を記載。以下、個人的な都合の理由で英語のまま記載。

Assume you've had n classes and your GPA is g. Let x be the number of 4.0s needed to offset a single grade of 3.2. Then to find x we must solve the equation
total grade points/total number of classes = 3.9
The denominator is just n + 1 + x. The n comes from the classes you've already had, the 1 is the class with the 3.2, and the x comes from the classes you will take in the future (that you will get a 4.0 in).

In order to find the numerator, you need to use
Total grade points = Grade points from past classes + 3.2 + Grade points from future classes

The first term is just ng, because the definition of average says that
g= grade points from past classes/n

The third term is 4x, because you will get 4 grade points for each of your x future classes.

Putting this all together, we have
ng + 3.2 + 4x/n + 1 + x = 3.9
ng + 3.2 + 4x = 3.9n + 3.9 + 3.9x
0.1x = 3.9n - ng + 0.7
x=n(39 - 10g) + 7

which is our final answer.

Analysis:

If the 3.2 is our first grade ever and we haven't taken any other classes, n is 0 and x = 7. This agrees with his answer.
If 10g < 39 (i.e. g < 3.9), then the larger n is, the larger x becomes. This means that if you have less than a 3.9 GPA to begin with, then the more classes you've already taken, the more classes you must take to offset your current GPA. Makes sense, right?

But if 10g > 39 (i.e. g > 3.9), the opposite is true. The first term on the left hand side is negative, so the larger n is, the smaller x becomes. That is, if your GPA started above a 3.9, then the more classes you've already taken, the fewer 4.0s you must make to bring your GPA to a 3.9. If n is too large, then x becomes negative. You can interpret this by saying that if you have done well in too many classes, there's no way that getting more 4.0s will bring you to a 3.9, because you probably had more than a 3.9 despite your 3.2 in that class. ref: http://b.qr.ae/18ZRnsf