Application problem

Question

Each test is worth 100 points, your final is worth 150. Your HW grade is worth 50 points. Your final also replaces your worst exam. You scored 35 on the first exam, 65 on the second. You have 50 out of 50 on the HW (let's assume you earn all remaining points). What percentage will you need on both the last exam and final to earn a C (minimum needed is 70.5). Write an equation and solve.

Answer 1

Let:

T1=Test1 grade=35

T2=Test2 grade=65

T3=Test3 grade=y (variable, unknown)

F  =Final test grade=x (variable, unknown)

HM=Homework=50

4 total grades used to figure average final grade of "C" or 70.5.

 

 

Recognize that there are two cases to this prob:

 

Case1:  When 3rd test score T3 (y) is 0<y≤35.  If

            this is case, score T3 (y) will be dropped.

Case2:  When 3rd test score T3 (y) is 35<y≤100.  

            If this is case, the score of T1 (35) will be

            dropped.

 

Case1 Eqn:  

70.5=((T1+T2)+F+HW)/4....T3 (y) grade is dropped.

70.5=((35+65)+x+50)/4

Solve for x, get x=132=F.....meaning that Final max

                                         test grade (F) must be 

                                         132 if Test3 (T3) grade is

                                         minimum score of 0 to

                                         maximum score of 35.

 

Case2 Eqn:

70.5=((T2+T3)+F+HW)/4...T1 (35) will be dropped if

                                         T3 (y) is a score of 35 to

                                         100.

70.5=((65+y)+x+50)/4...simplify....

x+y=167

    x=167-y

 

Now if y (T3) can only be maximum of 100, substitute, solve for x...

    x=67

which is minimum Final (F) when the maximum grade of 100 for T3 (y) is scored.  The equation x=167-y can be to calculate other "ordered pair" scores for T3 between 35 and 100.

 

Summary:

If Test3 scores between 0-35, Final maximum score must be 132.

If Test3 scores 100, Final minimum score must be 67.

Use F= 167-T3 for T3 scores between 35 and 100.