On two​ examinations, you have grades of 89 and 85. There is an optional final​ examination, which counts as one grade. You decide to take the final in order to

Question

On two examinations, you have grades of 89 and 85. There is an optional final examination, which counts as one grade. You decide to take the final in order to get a course grade of A, meaning a final average of at least 90.
a. What must you get on the final to earn an A in the course?
b. By taking the final, if you do poorly, you might risk the B that you have in the course based on the first two exam grades. If your final average is less than 80, you will lose your B in the course. Describe the grades on the final that will cause this to happen.

Answer 1

Let x = optional final score

 

     T = Total Scores = 89 + 85 + x 

 

     n =number of tests = 3

 

     T/n ≥ 90  or

 

     T/n = 90 to find minimum x 

 

     T = 90*n

 

     Substitute for T =  89 + 85 + x    and n = 3   and solve for x

 

    89 + 85 + x = 90*3 = 270

 

    x = 270 - 89 - 85 = 270 - 174 = 96

 

a)  x = 96

 

For part b):

 

T/n < 80

 

T < 80*n            n = 3

 

89 + 85 + x < 80*3

 

x < 240 - 89 - 85

 

x < 66

 

Therefore x must be less than 66,

 

However, since the grade has to be an integer; therefore,

 

if x ≤ 65 than you will lose your B grade

 

 

 

 

 

 

Answer 2

a.  In order to average 90 on all three tests, you need a total score of 270 or higher.  270 - (89+85) = 96

 

b.  Same process but you need 240 total points to keep the B  240 - (89+85) = 66