Question

If one-sixth of a number, plus one-third, returns two-thirds of that number, what is the number?

Answer 1

The number is
`(2)/(3)`.

Explanation:

Let the number be represented by t. Thus;

`(1)/(6)` of t +
`(1)/(3)` =
`(2)/(3)` of t

`(1)/(6)` x t +
`(1)/(3)` =
`(2)/(3)` x t

`(t)/(6)` +
`(1)/(3)` =
`(2t)/(3)`

Multiply through by 6.

t + 2 = 4t

2 = 4t - t

2 = 3t

⇒ t =
`(2)/(3)`

The number is
`(2)/(3)`.