GPA Question?

Corrected: At first. I using a wrongly used 4 credit course instead of 3 credit course. After the correction, you get the same answer.

I misread your original question.

If you are on a 4 point scale, A=4, B=3, C=2, D=1 , F=0

You were not very helpful, since you did say whether you got your "A" in one of the 3 or 6 credit course.

GPA= (sum of each grade*number of credit hour) / (total number of credit hours.)

x= grade in 6 hour course

y and z = grades in the 3 hour courses,

GPA = (6*x+ 3*y+3*z)/(6+3+3) = (6*x+3*y+3*z) / 12

12*3.6= 6*x+ 3*y+ 3*z

43.2= 6x+3y+3z

divide by 3

43.3/3= 2x+y+z

14,4= 2x +y +z

Case 1: The course you already got an "A" was 3 hour course

if the course you already got an A in was a three hour course , then

14,4 = 2x +y + 4

10.4= 2x + y

so in this case

if you got a B in the 6 hour course

10.4= 2*3+y

10.4 - 6 = y

4.4=y since you can't score as high 4.4 in any class, this indicate that you must get an "A" in your 6 hours course.

So now what if you got an "A" in your . 6 hours course, what is the lowest grade you could get in the 3 hours course remaining.

14.4 = 2x +y + 4

10.4 = 2*4+y

y=10.4- 8 = 2.4 , but you can only have a 2 or a 3 or 4 , so you must have a B or higher.

TO summarize, this case,

IF the course you already got an A was a 3 hour course, you must have an "A" in your six hours course and can have an "A" or "B" in your 3 hours course.

2nd Case: The course you already got the "A" was the 6 hour course

14.4 = 2*4 +y +z

14,4 = 2*4+ y+z

14.4 - 8= y+z

6.4 = y+ z

To add up to bigger than 6.4 , you need a 4 and 3 .

So in this case too, you need one "A" and one "B".

=== Summary =====

In total summary, if the course you already got an "A" was a four hour course, you need an "A" in the six hour course and "B" or higher in the 3 hour course.

If the course you already got an "A" was the six hour course, you need an "A" in one of the three hour course and "B" or higher in the other 3 hour course.

=== checking results

A - in 6 hour

B- in one 3 hour

A in one 3 hours

GPA= (4*6 + 3*3 + 4*3) / 12 = (24+9+12) /12 = (45/12) = 3.75

== A in 6 and two B in other 3

GPA_not_3.6= ( 6*4+ 3*3+3*3)/12= (24+18) /12 = 42/12 = 3.5 (not good enough for 3.6)