SOLUTION: If the average (arithmetic mean) of four different positive integers is 50, what is the greatest value of one of the integers?

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Question 198689: If the average (arithmetic mean) of four different positive integers is 50, what
is the greatest value of one of the integers?
Found 2 solutions by jim_thompson5910, arallie:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28w%2Bx%2By%2Bz%29%2F4=50 Start with the average equation. We'll make "z" the largest number.


w%2Bx%2By%2Bz=50%2A4 Multiply both sides by 5.


w%2Bx%2By%2Bz=200 Multiply


z=200-w-x-y Solve for "z"


z=200-%28w%2Bx%2By%29


So for "z" to be a maximum, the value of w%2Bx%2By must be a minimum. Since the integers are positive and the smallest positive integer is 1, this means that w=x=y=1 which means that w%2Bx%2By=3. So....



z=200-3=197

This means that the largest integer is 197.

Answer by arallie(162) About Me  (Show Source):
You can put this solution on YOUR website!
Here we go:
If %28a%2Bb%2Bc%2Bd%29%2F4=50 when %22%28a%2Cb%2Cc%2Cd%29%22%3E=1 and %22%28a%2Cb%2Cc%2Cd%29%22=int%28%22%28a%2Cb%2Cc%2Cd%29%22%29 and a%3C%3Eb%3C%3Ec%3C%3Ed
Ifa%3Cb%3Cc%3Cd and %28a%2Bb%2Bc%2Bd%29%2F4=50
Then %28a%2Bb%2Bc%2Bd%29=200
If a=1, b=2, c=3 as the lowest positive integers possible in %28a%2Bb%2Bc%2Bd%29=200
Then %281%2B2%2B3%2Bd%29=2006%2Bd=200d=194
Highest possible integer when 4 positive integers are averaged is 194.
Anymore questions feel free to ask me.
Anthony Allie
arallie@gmail.com
http://arallie.webs.com/tutoring.htm