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.

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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

give me the answer

Answer 2

To find the difference between the highest possible overall grade point average and the lowest possible overall grade point average, we need to determine the grade point value for each of Jared's grades and then calculate the averages.

The grade point values are as follows:
- A: 4.0 points
- B: 3.0 points
- C: 2.0 points
- D: 1.0 point
- F: 0 points

Jared's first six grades are as follows:
- 2 A's
- 3 B's
- 1 C

Let's calculate the highest and lowest possible overall grade point averages for these grades:

Highest possible overall grade point average:
If Jared gets an A in his seventh class, he will have a total of 6 A's, 3 B's, and 1 C. Adding up the grade point values, we get:
(6 * 4.0) + (3 * 3.0) + (1 * 2.0) = 24.0 + 9.0 + 2.0 = 35.0
To calculate the average, we divide the total grade point value by the total number of classes:
35.0 / 7 = 5.0

Lowest possible overall grade point average:
If Jared gets an F in his seventh class, he will have a total of 6 A's, 3 B's, 1 C, and 1 F. Adding up the grade point values, we get:
(6 * 4.0) + (3 * 3.0) + (1 * 2.0) + (1 * 0) = 24.0 + 9.0 + 2.0 + 0 = 35.0
To calculate the average, we divide the total grade point value by the total number of classes:
35.0 / 7 = 5.0

Therefore, the positive difference between the highest possible overall grade point average and the lowest possible overall grade point average is 5.0 - 5.0 = 0.