To receive a B in a course, you must have an average of at least 80% but less than 90% on five exams...

Question

To receive a B in a course, you must have an average of at least 80% but less than 90% on five exams. Your grades on the first four exams were 95%, 79%, 91%, and 86%. What range of grades on the fifth exam will result in a B for the course? Show your work.

Answer 1

80  ≤  B grade  < 90       ["at least" means ≤]

 

80 ≤ (95 + 79 + 91 + 86 + x) / 5  < 90                [assume equal weights for exams]

 

  80 ≤ (351 + x) / 5 < 90                           [add values]

  400 ≤ (351 + x) < 450       [multiply by 5 retains sense of inequality]

   49 ≤ x < 99                    [subtract 351 retains sense of inequality]

 

The exam grade must be at least 49 but less than 99 to get a B average.

Answer 2

x = minimum grade

 

80 = (1/5)(95 + 79 + 91 + 86 + x)

 

400 = 351 + x

 

x = 400 - 351 = 49

 

y = maximum grade:

 

90 = (1/5)(95 + 79 + 91 + 86 + y)

 

450 = 351 + y

 

y = 450 - 351 = 99

 

The range for the score is:

 

49 ≤ score < 99