Think of a Number/Examples/Rhind Papyrus 30

Example of Think of a Number puzzles
Problem $30$ of the is as follows:
 * If the scribe says to thee:
 * $10$ has become $\dfrac 2 3 + \dfrac 1 {10}$ of what?

Solution
This can more clearly be expressed as:


 * I think of a number.


 * $\dfrac 2 3$ of that number plus $\dfrac 1 {10}$ of it make $10$.


 * What number did I think of?

The number was $13 + \dfrac 1 {23}$.

Proof
Let $x$ be the number first thought of.

We have: