Method of False Position

Problem: A quantity, its half, its fourth and its eighth are added together to give 15. What is the quantity?


Modern Solution: (x) + (x/2) + (x/4)+ (x/8) = 15

                             (8x/8) + (4x/8) + (2x/8) + (x/8) = 15

                             (8x + 4x + 2x + x)/8 = 15

                             (15x)/(8) = 15

                              15x = 120

                               x = 8


Egyptian "False Position" Solution: Try x = 16

                                                                    = (16) + (16/2) + (16/4)+ (16/8)

                                                                    = 16 + 8 + 4 + 2 

                                                                    = 30

We need an answer that is 15, which is half. So, x must be half the trial number. ( 16 x (1/2) = 8)

Check: x = 8 

               = (8) + (8/2) + (8/4)+ (8/8)

               = 8 + 4 + 2 + 1

               = 15

Solved.

                                                             

                                                                  

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