SOLUTION: The average age of 8 men is increased by 2 years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is-

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Question 427278: The average age of 8 men is increased by 2 years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is-
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let %28sum%28x%5Bi%5D%2C+i+=+1%2C+8%29%29%2F8+=+x be the average age of the original 8 men.
Let alpha = average age of the two new men.
<==> %28sum%28x%5Bi%5D%2C+i+=+1%2C+6%29+%2B+21%2B+23%29%2F8+=+x
<==> %28sum%28x%5Bi%5D%2C+i+=+1%2C+6%29+%2B2alpha+%2B+44+-+2alpha%29%2F8+=+x
<==> %28sum%28x%5Bi%5D%2C+i+=+1%2C+6%29+%2B2alpha%29%2F8+%2B+%2844+-+2alpha%29%2F8+=+x
<==> +x%2B2+%2B+%2844+-+2alpha%29%2F8+=+x
<==> 2+%2B+%2844+-+2alpha%29%2F8+=+0
Solving for alpha, we get alpha+=+30, the average age of the two new men.