What is the largest possible integer that can be chosen as one of five distinct positive integers whose average is 10?
Details and assumptions
The elements of a set are distinct, if no two of them are the same.
the numbers have to sum to 50
so, picking the 4 smallest values as
1,2,3,4 which sum to 10, the largest 5th number is 40
To find the largest possible integer, we need to consider the average of the five distinct positive integers and work backwards.
Given that the average is 10, the sum of the five distinct positive integers must be 5 multiplied by 10, which is 50.
Since the numbers are distinct, the largest possible integer will be the closest to 50 without exceeding it.
To find the largest integer, we can start by subtracting the smallest four integers from 50, leaving us with the largest integer.
Let's assume the smallest four integers are a, b, c, and d. We need to find the largest possible value for e, such that a + b + c + d + e = 50.
Based on the assumption that the integers are distinct, a, b, c, and d will be the four smallest positive integers possible.
The smallest four positive integers are: 1, 2, 3, 4.
Substituting these values into the equation, we have:
1 + 2 + 3 + 4 + e = 50
10 + e = 50
e = 50 - 10
e = 40
Therefore, the largest possible integer is 40, under the given conditions.