Final answer:
To find the largest possible value of a number in a set of 6 positive integers with an average of 1000, where the smallest number is 151, we calculate the total sum, subtract the smallest integer and the smallest possible values for the other integers to maximize the largest integer which computes to 5241.
Step-by-step explanation:
The student has asked about the largest possible value of a number in a set of positive integers where the average is 1000 and the smallest number is 151.
To find the largest possible number, we must first calculate the total sum of all the numbers in the set by multiplying the average by the number of integers in the set. Since the average is 1000 and there are 6 numbers, the total sum is 6 * 1000 = 6000.
After setting aside the smallest number, which is 151, the remaining sum to be divided among the other 5 integers is 6000 - 151 = 5849. To maximize the largest integer, the other four integers should be as small as possible, so we'll assume they are one more than the smallest, which is 152. Thus, the sum of these four integers would be 4 * 152 = 608. Therefore, the largest integer would be 5849 - 608 = 5241.