Word problem

Question

Robert knows from reading his syllabus in intermediate algebra that the average of his chapter tests accounts for 80% (0.8) of his overall course grade. He also knows that the final exam counts as 20% (0.2) of his grade. Suppose that the average of Robert’s chapter tests is 89%. Determine the range of grades that he would need on his final exam to get an “A” in the class. (Assume that a grade of “A” is obtained if Robert’s overall average is 90% or better.)

Answer 1

The "weight" of Robert's chapter tests is 0.8 and he got 89% of the maximum for that.   0.8*(89%) is 71.2

 

The weight of Robert's final exam is 0.2 and he must get x% of that.    0.2*x

 

For an "A" grade, Robert's weighted average must be:

     (weighted average) ≥ 90%

  (weighted average for chapter tests) + (weighted average for final) ≥ 90%

 

     0.8*(89%) + 0.2(x%) ≥ 90%

       71.2% + 0.2x% ≥ 90%

            0.2x% ≥ 18.8%

              x% ≥ 94%

 

If Robert scores 94% or better on his final, he will get a "A."

 

Note: If Robert had scored 100% on his tests and would get 100% on his final, this would be:

             (0.8)*100% + (0.2)*100%

             80% + 20%

              100%

Answer 2

We can solve this problem by doing a weighted average. So the set up will look like this:

 

[Weight of chapter test grades]*[chapter test average] + [Weight of final exam]*[final exam score] = [Overall average]

 

So now we substitute in:

 

0.8 * 0.89 + 0.2 * [final exam score] ≥ 0.9 (greater than or equal to 0.9 because he wants to get 90% or better)

 

0.712 + 0.2 * [final exam score ] ≥ 0.9 [multiply 0.8 and 0.89]

0.2 * [final exam score] ≥ 0.188 [subtract 0.712 from both sides]

[final exam score] ≥ 0.94 [divide both sides by 0.2]

 

So Robert must get a 94% or better on his final exam to get an A in the class.