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#33245

applications

inequalities

hard

90 sec

The average (arithmetic mean) of a set of numbers is the sum of the numbers divided by the count of the numbers. A student has taken $n$ quizzes. The sum of the scores on the first $n - 1$ quizzes is 1900. The score on the $n$ -th quiz is 100. If the student's average score for all $n$ quizzes must be at least 80, what is the maximum possible integer value of $n$ ?

• Up to 5 characters (6 if negative). Only numbers, decimal (.), fraction (/), negative (-).
• Fractions must be in lowest terms.
• Mixed numbers must be converted to improper fractions.