SOLUTION: The arithmetic mean of 6 numbers is 17. If two numbers are added, the new set of numbers will have an arithmetic mean of 19. What are the two numbers if their difference is 4? add

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Question 200815: The arithmetic mean of 6 numbers is 17. If two numbers are added, the new set of numbers will have an arithmetic mean of 19. What are the two numbers if their difference is 4?
additional question: how do you find the extremes anyway?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The arithmetic mean of 6 numbers is 17.
If two numbers are added, the new set of numbers will have an arithmetic mean of 19.
What are the two numbers if their difference is 4?
:
Mean is the same as average.
:
Let the two number be x & y
:
Write an equation for each statement:
;
"If two numbers are added, the new set of numbers will have an arithmetic mean of 19."
%286%2817%29+%2B+x+%2B+y%29%2F8 = 19
%28102+%2B+x+%2B+y%29%2F8 = 19
Multiply both side by 8, results
x + y + 102 = 152
x + y = 152 - 102
x + y = 50
:
"What are the two numbers if their difference is 4?
x - y = 4
x = (y+4)
:
Substitute (y+4) for x in the 1st equation, find y
(y + 4) + y = 50
:
2y = 50 - 4
y = 46%2F2
y = 23 is one number
then
x - 23 = 4
x = 27 is the other number
;
:
Check solution
%28102+%2B+27+%2B+23%29%2F8 =
152%2F8 = 19
:
:
Did this make sense to you? Any questions