SOLUTION: If I have an average grade of a 73 how can I get a 77?

Question 735620: If I have an average grade of a 73 how can I get a 77?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

That depends on how many scores you have that made up the average of 73, how many opportunities to score in excess of your current average that remain (and that could be single opportunities that have multiple weight, as in when you have a final that counts for 2 or more regular tests) and the maximum score attainable on each of your remaining scoring opportunities. Symbolically, if

is the number of previous opportunities,

is the remaining opportunities, and

is the average score needed for the remaining opportunities in order to achieve a final average of 77, then the following relationship holds:

A little algebra music, Sammy:

Plug in the numbers and calculate. If

where

is the average of the maximum scores of the remaining scoring opportunities, then you can't get there from here.

For example, let's say that you have a 73 average on 5 tests and there is one test left, the final.

So all you have to do is score 97 on the final to get your required 77 average. But what if the 73 average was based on 6 tests and the maximum possible score on the final is 100? Then:

And you can see that 77 is not achievable. Of course, if you have only done 73 work all semester, what's the probability of writing 97 on the final?

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

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