Question

If one-sixth of a number plus one-third returns two-thirds of that number What is the number

Answer 1

`x= (2)/(3)`

Explanation:

Let the number be x

Given

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

Required

Find x

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

Collect Like Terms

`(1)/(6)x - (2)/(3)x = - (1)/(3)`

Take LCM

`(1 - 4)/(6)x = (-1)/(3)`

`(- 3)/(6)x = (-1)/(3)`

Multiply both sides by 6

`6 * (- 3)/(6)x = (-1)/(3) * 6`

`-3x= -2`

Divide both sides by -3

`(-3x)/(-3)= (-2)/(-3)`

`x= (2)/(3)`

Hence, the number is
`(2)/(3)`