SOLUTION: "Arithmetic Mean(A.M)" of a series of 15 values is 20. By adding two more values, it becomes 18. Find out the values added, if the ratio between them is 1 to 2.

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Question 681602: "Arithmetic Mean(A.M)" of a series of 15 values is 20. By adding two more values, it becomes 18. Find out the values added, if the ratio between them is 1 to 2.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
"Arithmetic Mean(A.M)" of a series of 15 values is 20. By adding two more values, it becomes 18. Find out the values added, if the ratio between them is 1 to 2. 
Let S = the sum of the 15 values, then

S%2F15 is the mean.  Therefore:


S%2F15 = 20

The two values added are in the ratio of 1 to 2, which means
that one is twice the other.  So 

let the smaller of the two be x
Then the larger of the two is 2x

So if we add those two, the new sum will be S + x + 2x, and there
will be 15+2 or 17 numbers in the new sequence,

So we have the second equation:

%28S%2Bx%2B2x%29%2F17 = 18

Therefore we have this system of equations:

system%28S%2F15+=+20%2C+%28S%2Bx%2B2x%29%2F17+=+18%29

Simplify the second by adding x+2x and getting 3x

system%28S%2F15+=+20%2C+%28S%2B3x%29%2F17+=+18%29

Multiply the first by 15 and the second by 17

system%28S+=+300%2C+S%2B3x+=+306%29

Substitute 300 for S in the second:

300 + 3x = 306
      3x = 6
       x = 2

So the smaller number added is x or 2 and the larger is 2x or 4.

Edwin