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18 July, 09:49

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

+5
Answers (1)
  1. 18 July, 10:45
    0
    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

    2

    x

    then

    2

    x

    +

    1

    2

    x

    =

    1

    2

    4

    x

    +

    x

    2

    x

    2

    =

    1

    2

    10

    x

    =

    2

    x

    2

    2

    x

    2

    -

    10

    x

    =

    0

    2

    x

    (

    x

    -

    5

    )

    =

    0

    Zero is not viable solution as its reciprocal is infinity. The answer is therefore

    x

    =

    5
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