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.