SOLUTION: the average of 11 results is 30,that of the first five is 25 and that of the last five is 28.the value of 6th number is?

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Question 776674: the average of 11 results is 30,that of the first five is 25 and that of the last five is 28.the value of 6th number is?
Answer by AnlytcPhil(1807) About Me  (Show Source):
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the average of 11 results is 30,that of the first five is 25 and that of the last five is 28.the value of 6th number is? 
Let the 11 results be a,b,c,d,e,f,g,h,i,j,k

>>...the average of 11 results is 30,...<<
%28a%2Bb%2Bc%2Bd%2Be%2Bf%2Bg%2Bh%2Bi%2Bj%2Bk%29%2F11%22%22=%22%2230

Multiply both sides by 11

a+b+c+d+e+f+g+h+i+j+k = 330

>>...that of the first five is 25,...<<
%28a%2Bb%2Bc%2Bd%2Be%29%2F5%22%22=%22%2225

Multiply both sides by 5

a+b+c+d+e = 125

>>...and that of the last five is 28...<<
%28g%2Bh%2Bi%2Bj%2Bk%29%2F5%22%22=%22%2228

Multiply both sides by 11

g+h+i+j+k = 140

So we have these three equations:

a+b+c+d+e+f+g+h+i+j+k = 330
a+b+c+d+e             = 125
            g+h+i+j+k = 140

Subtract the 2nd equation from the 1st:

          f+g+h+i+j+k = 205

Subtract the third equation from that

          f+g+h+i+j+k = 205
            g+h+i+j+k = 140
          f           =  65

Answer 65.

Edwin