When asked what her math average was, a student coyly responded: "I've taken four tests to date and when I add the highest score with my lowest score and divide the result by the sum of my other two scores, I get a ratio of 1.4"

Assuming all scores are equally weighted and each grade is a real number between 0 and 100 inclusive, find four scores that produce the highest possible average (arithmetic mean), and show that a higher average is not possible.

(In reply to re(2): Question. by Bractals)

I originally worked the problem out assuming the scores were integers, and then reworked it when I re-read the problem and saw that each grade was a real number.  If you restrict it to just integers, then I think the answer is 100, 55, 55, and 54, not drastically different obviously.

And there are many times I've gotten non-integer scores on tests - for example, what grade would you receive if you answered 14 questions correctly on a test with 16 questions? 

Posted by tomarken on 2006-12-10 13:22:16