SOLUTION: the average age of 8 men is increased by 2 when two men of 21 yrs and 23 yrs are replaced by two new men.what is the average of ages of two new men?????

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Question 474940: the average age of 8 men is increased by 2 when two men of 21 yrs and 23 yrs are replaced by two new men.what is the average of ages of two new men?????
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The average age of 8 men is increased by 2, when two men of 21 yrs and 23 yrs are replaced by two new men.
what is the average of ages of two new men
:
Total age of the new men is 44
:
Let a = total age of the 6 men that are unchanged
then
(a+44) = total age of the 8 men originally
and
%28a%2B44%29%2F8 = original average age
:
let b = total age of the 2 new men
then
%28a%2Bb%29%2F8 = new average age
:
the equation for the given statement
:
New average = old average + 2
%28a%2Bb%29%2F8 = %28a%2B44%29%2F8 + 2
multiply by 8
a + b = a + 44 + 16
Subtract a from both sides
b = 44 + 16
b = 60 is the total age of the two new men
and
60%2F2 = 30 is the average age of the two new men
:
:
We can check this with real numbers if we can find a, but it's on both sides of
the equation so let's just assume a=124, (the total age of the 6 men)
%28124%2B60%29%2F8 = %28124%2B44%29%2F8 + 2
184%2F8 = 168%2F8 + 2
23 = 21 + 2