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CASE 1

A hypothetical student has 115 points out of 120 in the laboratory, and the following four exam scores:

     Exam 1: 40
     Exam 2: 75
     Exam 3: 62
     Exam 4: 73

What score does she need on the final exam in order to get a B- in the course?

To earn a B-, at least 496 points (80%) out of the possible 620 points are needed.  Her lowest score is the Exam 1 score--a "40."

That score will be replaced by her final exam score, provided the final exam score is higher than 40.

What does the final exam score have to be?

Let the necessary final exam score be represented by "x." The sum of the four exam scores, plus the final exam score, plus the 115 lab score is given below:

     x + 75 + 62 + 73 + x + 115

This simplifies to

     2x + 325

She needs at least 496 points to earn a B-, so what value of x will give her this total score?

     2x + 325 = 496

Solving for x, we get

     x = 85.5

This rounds up to 86. She needs to get an 86 on the final exam in order to get a B- in the course.



CASE 2

A student's exam scores are listed below, and he wants to know what score he needs to get on the final exam in order to earn a "C-" in the course.     

     Exam 1: 35
     Exam 2: 55
     Exam 3: 65
     Exam 4: 52

This student's laboratory score is 112.

If a student is in jeopardy of getting a score less than the 70% (434 points) needed for a C- even if one of his low exam scores in replaced by the final exam score, the "two replacement rule" is applied: the student's two lower exam scores will be replaced by the final exam score (assuming the final exam score is higher than each of the two lower scores).

What score does this student need on the final?

Call the unknown score "x."

Exam 1 and Exam 4 will replaced by "x," and the sum of the student's four exam scores, plus the final exam score, plus the 112 lab score, is given below:     

      x + 55 + 65 + x + x + 112

This simplifies to     

      3x + 232

He needs at least 434 points to earn a C- in the course:     

      3x + 232 = 434

Solving for x, we get

      x = 67.33

This rounds up to 68. This student needs to get a 68 or higher on the exam in order to get a C- in the course.

 

CASE 3

A student's first three exam scores are very low, and she wants to know how well she has to do on the fourth exam and the final in order to earn a C- in the course (434 points).

Her lab scores have been good, and she expects that she will finish the semester with 116 points out of 120 in the lab.

Here are her three exam scores:

     Exam 1: 40
     Exam 2: 46
     Exam 3: 49

To simplify the calculation, we assume that her scores on the fourth exam and the final will be the same. We will call that score "x."

Using the "two replacement rule," the student's two lower exam scores are replaced by the final exam score.

After replacing the first two exam scores above with "x," and setting the score for Exam 4 to be "x" as well, the sum of her four exam scores, plus the final exam score, plus the 116 lab score is

     x + x + 49 + x + x + 116

This simplifies to

      4x + 165

She needs at least 434 points to get a C- in the course.

What does x have to be?

     4x + 165 = 434

Solving for x, we get

     x = 67.25

This rounds up to 68. This student needs to get a 68 on the final in order to get a C- in the course.