Think of a Number/Examples/Rhind Papyrus 33

Example of Think of a Number puzzles
Problem $30$ of the is as follows:
 * A number, plus its two-thirds, and plus its half, plus its seventh, makes $37$. What is the number?

It is to be expressed in Egyptian form.

Solution
This can more clearly be expressed as:


 * I think of a number.


 * If you add $\dfrac 2 3$ of that number plus $\dfrac 1 2$ of that number and $\dfrac 1 7$ of that number, you get $37$.


 * What number did I think of?

The number was $16 + \dfrac 1 {56} + \dfrac 1 {679} + \dfrac 1 {776}$.

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

We have: