Trying to figure out test scores.

Question

You take a 14 week course in which your overall test score must average at 70% or above. The first 13 weeks, you take 9 tests. The 14th week, you take a comprehensive final makes up 30% of your overall test score average. How can you find out what you need to score on the comprehensive final to keep a 70% test score average based on the test score average of the 9 tests previously taken?

Answer 1

The previous 9 assignment comprise 70% of the grade.

Let M be the average of these 9 assignments, where 0 < M < 100

 

 

 0.7M + 0.3X >=70

 

 7M + 3X >= 700

 

 3x >= 700 - 7M

 

 x >= (700 - 7M)/3

 

So if your average is M=70, then X >= (700 - 7*70)/3 = (700 - 490)/3 = 210/30 = 70

     If the average is M=80, then X >= (700 - 7*80)/3 = ( 700 - 560)/3 = 140/3 = 46 and 2/3

   If the average is M=60, then x >= (700 - 7*60)/3 = (700 - 420)/3 = 280/3 = 93 and 1/3