Finite Math Question?

Question

Students at ACC must earn 90 credits to obtain an Associate’s degree. Three students find that they all have a GPA of 3.3 even though they do not have the same number of credits. The students hope to increase their GPAs to a 3.8 by the time they have earned 90 credits. One student has earned 50 credits, another has earned 40, and the other, 85. Is it possible for all of the students to increase their GPA by the time they earn 90 credits?

Answer 1

To earn a 3.8 GPA, a student must earn an average of 3.8 'grade points' for 90 credits.  This means they must earn 342 grade points (90*3.8) at the end of their degree.

The student who has earned 50 credits and averaged 3.3 has earned 50*3.3=165 grade points so far.  He/She needs to earn 342-165 or 177 more grade points.  However, the maximum he/she can earn is 4*40=160 more grade points.  

The student who has earned 40 credits and averaged 3.3 has earned 40*3.3=132 grade points so far.  He/She needs to earn 342-132 or 210 more grade points. However, the maximum that he/she can earn is 4*50=200 grade points.

The student who has earned 30 credits and averaged 3.3 has earned 30*3.3=99 grade points so far.  He/She needs to earn 342-99 or 243 more grade points.  However, the maximum that he/she can earn is 240 grade points.  If this student earns all A's on his/her remaining classes, he/she will have (99+240)/90=339/90=3.76 for his/her GPA.

It's too late for any of these three students to earn a 3.8 GPA before they earn 90 credits, unless classes can be re-taken for higher grades but no extra credit.

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