Egyptian Algebra: 'Method of False Position'

Here is my sample word problem:

By 2050, it is estimated that there will be a one-third decline in the polar bear population. If there are 16000 polar bears left, how many were there to start with?

Modern Method:

16000 = x - x/3

48000 = 2x

24000 = x

Thus, there were 24000 polar bears to start with. 

False Position:

(To keep the numbers simple, we’ll scale it down by 1000.)

A number minus its third is equal to 16: 16 = x - x/3

We need an initial value, so let's guess that x =18. This results in (18) - (18/3) = 12.

This guess is off by a multiple of 4/3, so we multiply our guess by that multiple.

18 x (4/3) = 24.

Confirming our answer: (24) - (24/3) = 16. Hence, x = 24 is correct.

This means that there were 24 (x 1000) polar bears to start with.