the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 16 , and k < m < r < s < t . if t is 30 , what is the greatest possible value of the median of the 5 integers ?
"we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 16 which means that in effect , all numbers are equal to 16 . if the largest number is 30 , it is 14 more than 16 . we need r to be maximum so k and m should be as small as possible to get the average of 16 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 15 less than 16 and 2 is 14 less than 16 which means k and m combined are 29 less than the average . 30 is already 14 more than 16 and hence we only have 29 - 14 = 15 extra to distribute between r and s . since s must be greater than r , r can be 16 + 12 = 28 and s can be 16 + 13 = 29 . so r is 28 . answer ( e )"
subtract(divide(subtract(multiply(16, 5), 30), const_2), const_2)