The reciprocal of half a number increased by half the reciprocal of the number is 1/2. what is the number?

1 Answer
Roella W.
Dec 23, 2015

5

Explanation:

Let the number equal x. Half the number is then #x/2# and the reciprocal of that is #2/x#
The reciprocal of the number is #1/x# and half that is #1/(2x)#
then #2/x + 1/(2x) = 1/2#
#(4x +x)/(2x^2) = 1/2#
#10x = 2x^2#
#2x^2 -10x = 0#
#2x(x-5) = 0#
Zero is not viable solution as its reciprocal is infinity. The answer is therefore #x=5#

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