What is the largest possible integer that can be chosen as one of five distinct positive integers whose average is 10?
To find the largest possible integer that can be chosen as one of five distinct positive integers whose average is 10, we need to understand the concept of average.
The average of a set of numbers is the sum of all the numbers divided by the total count of numbers.
Let's denote the five positive integers as A, B, C, D, and E. Since we want to find the largest possible integer, let's assume that E is the largest integer.
Now, we know that the average of these five integers is equal to 10. Mathematically, we can express this as:
(A + B + C + D + E) / 5 = 10
To simplify this equation, we can multiply both sides by 5 to eliminate the denominator:
A + B + C + D + E = 50
Since we want to find the largest possible value for E, we can assign the smallest values (1, 2, 3, and 4) to the other variables:
1 + 2 + 3 + 4 + E = 50
Simplifying this equation, we get:
10 + E = 50
Finally, subtracting 10 from both sides, we find:
E = 40
Therefore, the largest possible integer that can be chosen is 40.