Question

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

Answer 1

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`