SOLUTION: In a list of positive integers, the arithmetic mean is 5, and the number 16 is known to appear. If the 16 is removed, the mean drops to 4. What is the largest possible number that

Question 1013719: In a list of positive integers, the arithmetic mean is 5, and the number 16 is known to appear. If the 16 is removed, the mean drops to 4. What is the largest possible number that could occur in the original list?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
In a list of positive integers, the arithmetic mean is 5, and the number 16 is known to appear.
If the 16 is removed, the mean drops to 4.
What is the largest possible number that could occur in the original list?
:
let n = no. numbers in the list not counting the 16
We know the value of those numbers have to be 4n
= 5
4n + 16 = 5(n+1)
4n + 16 = 5n + 5
16 - 5 = 5n - 4n
n = 11
therefore
the total value of those numbers are: 4*11 = 44
It you include 16, you have 12 numbers, total value is 60, for an average is 5
:
"What is the largest possible number that could occur in the original list?"
If the first 10 numbers were equal to 1, the 11th number could be = 34, the highest integer.

RELATED QUESTIONS
A list of 5 positive integers has all of the following properties: the only integer in... (answered by greenestamps,math_helper)

If S is a set of 5 positive, distinct integers with an average (arithmetic mean) of 9 and (answered by Edwin McCravy)

The mean of 6 numbers is 16. With the removal of a number the mean of remaining numbers... (answered by ewatrrr)

What is the arithmetic mean (ordinary average) of the 73 successive positive integers,... (answered by ikleyn)

If the average (arithmetic mean) of three numbers is 6, and the sum of the two larger... (answered by ankor@dixie-net.com)

Could you please help me with this question?: The average (arithmetic mean) of ten... (answered by Alan3354)

The squares of three positive integers are in arithmetic progression, and the third... (answered by ikleyn,greenestamps)

the mean of ten positive numbers is 16. When another number is added the mean is 18. find (answered by ikleyn,greenestamps)

The avg arithmetic mean of 5 different integers is 100.If the largest integer is 120 what (answered by ikleyn)