Method of False Position

Problem: A quantity and its twice are subtracted from the quantity and it's ninth, give 34. What is the quantity? 

Modern Approach: 2x - (x/9) = 34

                               (18x-x)/9 = 34

                                     17x    = 306

                                        x     = 18

Egyptian Approach: let x=9, which is easier as it makes 9/9=1. 

                                     2(9)-(9/9) = 18-1 = 17. 

We need the answer to be 34, which is twice as big as 17. 

So x must be twice as big as the trail number. (2x9=18)

Lets check: If x=18, 2x-x/9 = 36 - 18/9

                                             = 36-2

                                             = 34. 

Thus solved!