SOLUTION: A list of 5 positive integers has all of the following properties: the only integer in the list that occurs more than once is 8, its median is 9, and the mean is 10. What is the la

Question 1144770: A list of 5 positive integers has all of the following properties: the only integer in the list that occurs more than once is 8, its median is 9, and the mean is 10. What is the largest possible integer that could appear on this list.
Found 2 solutions by greenestamps, math_helper:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

(1) There are 5 integers; in order they are A, B, C, D, and E.

(2) The median is 9: A, B, 9, D, E

(3) 8 is the only number that occurs more than once: 8, 8, 9, D, E

(4) The mean is 10: (8+8+9+D+E)/5 = 10 --> D+E = 25

The largest possible value for E is when D is as small as possible. Since only 8 occurs more than once, D should be 10; that makes E 15.

ANSWER: 15
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!

The list is 8,8,9,10,x

The rationale:
1. We are told there is more than one 8
2. The median is 9 (so thie middle number is 9, here middle comes 3rd)
3. 10 is the 4th number because we want to maximize x
( x + 8 + 8 + 9 + 10 ) / 5 = 10
x + 35 = 50
x = 15
Ans: 15 is the largest possible integer that can appear on the list

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