SOLUTION: The number x is the harmonic mean of a and b if (1/x) is the average of (1/a) and (1/b). The harmonic mean of two numbers is 8. If one of the numbers is 5, find the other number.

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Question 409424: The number x is the harmonic mean of a and b if (1/x) is the average of (1/a) and (1/b). The harmonic mean of two numbers is 8. If one of the numbers is 5, find the other number.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
If x is the other number, then

HM+=+8+=+2%2F%281%2F5+%2B+1%2Fx%29 (this is the definition of harmonic mean that I learned and use. Either definition is fine.)

Cross-multiplying,

1%2F5+%2B+1%2Fx+=+1%2F4.

1%2Fx+=+1%2F4+-+1%2F5+=+1%2F20

x+=+20