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.

Question

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.

Given the previous information for Jared's first six grades, what is the lowest possible letter grade that Jared can earn in his seventh class to have an overall grade point average of at least 3.00 for the first grading period?

Answer 1

If the School Subject is MATH, please state that.

Sra

Answer 2

To find the lowest possible letter grade Jared can earn in his seventh class, we need to calculate his current overall grade point average and determine the minimum grade needed to achieve a GPA of at least 3.00 for the grading period.

First, let's calculate Jared's current overall grade point average (GPA) by converting his letter grades to their respective grade points:

- Jared earned a grade of A in two classes, which each have a 4.0 grade point.
- Jared earned a grade of B in three classes, which each have a 3.0 grade point.
- Jared earned a grade of C in one class, which has a 2.0 grade point.

To calculate the current overall GPA, we need to sum up the grade points and divide it by the total number of classes:

(2 * 4.0) + (3 * 3.0) + (1 * 2.0) = 8.0 + 9.0 + 2.0 = 19.0

Now, let's find the minimum grade Jared needs in his seventh class to achieve a GPA of at least 3.00. We can set up a proportion:

Current GPA / Total Classes = Target GPA / Total Classes (including the seventh class)

19.0 / 6 = Target GPA / 7

Target GPA = (19.0 / 6) * 7 = 19.0 * (7 / 6) = 22.83 (rounded to the nearest hundredth)

To calculate the minimum grade needed for the seventh class, we need to find the corresponding grade point for a GPA of 22.83. Since we are given a 4-point scale, we can set up the following inequality:

Grade Point ≤ (Target GPA / Total Classes) * 4

Grade Point ≤ (22.83 / 7) * 4

Grade Point ≤ 11.42

The minimum whole grade point that satisfies this inequality is 11. So, Jared needs a minimum grade point of 11 in his seventh class. In terms of letter grade, it corresponds to a grade of D (since a grade of D is worth 1.0 grade point).

Therefore, the lowest possible letter grade Jared can earn in his seventh class to have an overall GPA of at least 3.00 for the first grading period is a D.