Suppose A,B,C,D, and E are distinct positive integers such that A<B<C<D<E, their median is 10 and their mean is 15. Find the maximum possible value of D.
To find the maximum possible value of D, let's consider some facts about the given information:
Fact 1: The median of the numbers is 10. This means that C will be the middle number when the numbers are arranged in ascending order.
Fact 2: The mean of the numbers is 15. The mean is calculated by summing up all the numbers and dividing by the total count. In this case, we have 5 numbers (A, B, C, D, and E). Therefore,
(A + B + C + D + E) / 5 = 15
From this equation, we can rewrite it as:
A + B + C + D + E = 75
Fact 3: The numbers A, B, C, D, and E are distinct positive integers in ascending order.
Given these facts, let's try to find the maximum possible value of D.
Since C is the median and we want to maximize the value of D, let's assume the lowest possible values for the other numbers: A = 1, B = 2, and C = 10.
Substituting these values into the equation from Fact 2, we get:
(1 + 2 + 10 + D + E) / 5 = 15
Simplifying the equation, we have:
13 + D + E = 75
Now, let's try to maximize D by minimizing E. Assuming E is the smallest possible value, E = 3.
Substituting E = 3 back into the equation, we have:
13 + D + 3 = 75
Simplifying further, we get:
D = 75 - 16
Therefore, the maximum possible value of D is 59.
Thus, the maximum value of D in this case is 59.