SOLUTION: The reciprocal of half a number increased by half the reciprocal of the number is 1/2. Find the number.

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Question 996099: The reciprocal of half a number increased by half the reciprocal of the number is 1/2. Find the number.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The reciprocal of half a number increased by half the reciprocal of the number is 1/2.
Find the number.
:
let n = the number
then
.5n = half the number
:
1%2F%28.5n%29 + .5(1%2Fn) = 1%2F2
1%2F%28.5n%29 + .5%2Fn = 1%2F2
multiply equation by 2n
2n*1%2F%28.5n%29 + 2n*.5%2Fn = 2n*1%2F2
cancel the denominators and we have
4 + 2(.5) = n
5 = n
:
the number is 5