SOLUTION: the average of ten diffrent positive integers is 10.the smallest is 5.find the biggest possible number among these ten integers.

Question 475372: the average of ten diffrent positive integers is 10.the smallest is 5.find the biggest possible number among these ten integers.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
If the smallest member of the set is 5,
then the sum of the other 9 integers must be 95.
Now if we let the smallest integer among these 9 integers be 6,
consider the sum of the consecutive integers
6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 = 90.
To get a total of 95 we need to distribute 5 to some of the terms in the sum.
We can just add the 5 to 14, getting 19 as the biggest possible number among the ten integers.
Note that if we assume 7(or any higher integer)
as the smallest of the nine remaining integers,
then the sum of the consecutive integers would be greater than 95.
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