At Smart Middle School students are required to take 7 classes each grading period. At the end of each grading period a student is assigned a final grade (A, B, C, D or F) for each class for the grading period. A student’s overall grade point average for the grading period is determined using a 4-point scale, where a final class grade of A is worth 4.0 points, a B is worth 3.0 points, a C is worth 2.0 points, a D is worth 1.0 point and an F earns no points. Suppose Jared has learned his final grade for the first grading period for six of his classes. He earned a grade of A in two classes, a grade of B in three classes and a grade of C in one class. What is the positive difference between the highest possible overall grade point average and lowest possible overall grade point average that Jared can have for his seven classes? Express your answer as a decimal to the nearest hundredth.
Jared's highest possible GPA = (4.0*3 + 3.0*3 + 2.0*1)/7 = ?
Jared's lowest possible GPA = (4.0*2 + 3.0*3 + 2.0*1 + 0.0*1)/7 = ?
Subtract second answer from the first.
0.57
To find the highest possible overall grade point average (GPA), we need to assume that Jared earns an A in his remaining class. Since an A is worth 4.0 points, this would give Jared a total of 8.0 points for his two A grades.
To find the lowest possible overall GPA, we need to assume that Jared earns an F in his remaining class. Since an F earns no points, this would not contribute to his total points.
Now we can calculate the overall GPA for both scenarios and find the positive difference.
Highest possible overall GPA:
Jared earned a grade of A in two classes (worth 4.0 points each), a grade of B in three classes (worth 3.0 points each), and a grade of C in one class (worth 2.0 points). Assuming he earns another A in his remaining class, his total points would be:
(4.0 + 4.0 + 3.0 + 3.0 + 3.0 + 2.0 + 4.0) = 23.0
To find the GPA, we divide the total points by the number of classes:
23.0 / 7 = 3.29
Lowest possible overall GPA:
Jared earned a grade of A in two classes (worth 4.0 points each), a grade of B in three classes (worth 3.0 points each), and a grade of C in one class (worth 2.0 points). Assuming he earns an F in his remaining class, his total points would be:
(4.0 + 4.0 + 3.0 + 3.0 + 3.0 + 2.0 + 0) = 19.0
To find the GPA, we divide the total points by the number of classes:
19.0 / 7 = 2.71
Finally, we calculate the positive difference between the highest and lowest possible overall GPAs:
3.29 - 2.71 = 0.58
Therefore, the positive difference between the highest possible overall GPA and lowest possible overall GPA that Jared can have for his seven classes is 0.58.