College Algebra Word Problem

Question

On two examinations, you have grades of 85 and 93. 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 = score on the final

 

a.  To get an A, you must have (x+85+93)/3 ≥ 90

 

                                         So, x+178 ≥ 270

 

                                                     x ≥ 92

    You need at least a 92 on the final to get an A.  

 

b.  To avoid getting a grade of below a B, you must have                       

     (x+85+93)/3 ≥ 80

 

     (x+178) ≥ 240

 

              x ≥ 62

 

     As long as you get at least a 62 and below a 92, you will earn a B        for the course.  

 

Answer 2

F=final grade

(85+93+F)/3≥90

85+93+F≥270

178+F≥270

F≥270-178

F≥92 to earn an A

 

(85+93+F)/3<80

85+93+F<240

178+F<240

F<240-178

F<62 will cause you to lose your B