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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
For the 5 original conservative integers,
sum=5%2A8=40
Replacing the least number, x , with the largest one, y ,
the new sum is 40-x%2By=5%2A9.2 --> 40-x%2By=46 --> y=x%2B6
The other 3 numbers, x%2Ba , x%2Bb , and x%2Bc are in between.
The sum of all 5 numbers is
x%2B%28x%2B6%29%2B%28x%2Ba%29%2B%28x%2Bb%29%2B%28x%2Bc%29=40
5x%2B%286%2Ba%2Bb%2Bc%29=40 ,
Since 5x and 40 are both multiples of 5 ,
6%2Ba%2Bb%2Bc must also be a multiple of 5 .
Since all the numbers are different,
1%2B2%2B3%3C=a%2Bb%2Bc%3C=3%2B4%2B5 <---> 6%3C=a%2Bb%2Bc%3C=12 ,
so 12%3C=6%2Ba%2Bb%2Bc%3C=18 .
The only multiple of 5 between 12 and 18
is15 , so 6%2Ba%2Bb%2Bc=15 ,
5x%2B15=40 --> 5x=40-15=25 --> x=25%2F5=5 , and
y=5%2B6=highlight%2811%29 .