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 reread 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 noninteger 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 20061210 13:22:16 