SOLUTION: if average of 9 subject is 60 , if average of first five subject is also 60 and average of last 5 subject is 55 then what is the fitft number??

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Question 854671: if average of 9 subject is 60 , if average of first five subject is also 60 and average of last 5 subject is 55 then what is the fitft number??
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the sum of the 1st 4 numbers
Let +b+ = the 5th number
Let +c+ = the sum of the last 4 numbers
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(1) +60+=+%28+a+%2B+b+%2B+c+%29+%2F+9+
(1) +a+%2B+b+%2B+c+=+540+
----------------------------
(2) +60+=+%28+a+%2B+b+%29+%2F+5+
(2) +a+%2B+b+=+300+
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(3) +55+=+%28+b+%2B+c+%29+%2F+5+
(3) +b+%2B+c+=+275+
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(2) +a+=+300+-+b+
and
(3) +c+=+275+-+b+
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Substitute (2) and (3) into (1)
(1) +a+%2B+b+%2B+c+=+540+
(1) +300+-+b+%2B+b+%2B+275+-+b+=+540+
(1) +-b+%2B+575+=+540+
(1) +b+=+35+
The 5th number is 35
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check:
(2) +a+=+300+-+b+
(2) +a+=+300+-+35+
(2) +a+=+265+
and
(3) +c+=+275+-+b+
(3) +c+=+275+-+35+
(3) +c+=+240+
and
(1) +60+=+%28+a+%2B+b+%2B+c+%29+%2F+9+
(1) +60+=+%28+265+%2B+35+%2B+240+%29+%2F+9+
(1) +60+=+540%2F9+
(1) +540+=+540+
OK -you can check (2) and (3)