Question

Rob owns 3/5 of the stock in a local bread company. His sister Tailia owns half as much stock as Rob. What part of the stock is owned by neither Rob or Tailia?

Answer 1

Let 'x' and 'y' denote the part of stock owned by Rob and Tailia, respectively.

Give that Rob owns 3/5 of the stock,

`x=(3)/(5)`

Also it is given that Tailia owns half as much stock as Rob,

`\begin{gathered} y=(x)/(2) \\ y=(3)/(2*5) \\ y=(3)/(10) \end{gathered}`

So, Tailia owns 3/10 of the stock.

Now, it is known that the total stock must be unity,

`\text{Total Stock}=1`

Total stock must be the sum of stock holdings of Rob, Tailia, and other.

Then, the remaining part of stock which is neither owned by Rob, nor by Tailia, is calculated as,

`\begin{gathered} =\text{Total}-(x+y) \\ =1-((3)/(5)+(3)/(10)) \\ =1-(9)/(10) \\ =(1)/(10) \end{gathered}`

Thus, 1/10 of the stock is neither