If I have an average of 66% and that is worth 70% what do I need on the exam worth 30% to have an overall average of 70%

Question

If I have an average of 66% and that is worth 70% what do I need on the exam worth 30% to have an overall average of 70%?  And as well what is the calculation so I can use it in the future to figure out averages with different numbers or different weight factors?

Answer 1

 

x = total score for portion worth 70%

y = total score for portion worth 30%

 

       .7x + .3y = 70  

   .7(66) +.3y = 70

     46.2 + .3y = 70

                 .3y = 70 - 46.2

                 .3y = 23.8

                   y = 79.33

 

You need to score 79.33 %

  

Answer 2

You take a weighted combination of the averages:

 

66% of 70% is 0.66 * 70

 

You want to add x% of 30%, which in decimal form is (x/100) * 70

 

The sum of the above two must be at least 70%:

 

0.66(70) + (x/100)(30) ≥ 70

 

Solve for x and get x ≥ 79.34% (rounded slightly up)