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

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