SOLUTION: The average of 5 distinct whole numbers is 8. When the least number is replaced by a second copy of the largest number, the average is increased to 9.2. What is the largest possibl

Question 1061323: The average of 5 distinct whole numbers is 8. When the least number is replaced by a second copy of the largest number, the average is increased to 9.2. What is the largest possible number?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
For the 5 original conservative integers,

Replacing the least number, , with the largest one, ,
the new sum is --> -->
The other 3 numbers, , , and are in between.
The sum of all 5 numbers is

,
Since and are both multiples of ,
must also be a multiple of .
Since all the numbers are different,
<---> ,
so .
The only multiple of between and
is , so ,
--> --> , and
.
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