The method of 'false position' (estimate, check, adjust)

Problem:  Tom has a glass of water. He pours out three eighth of the water, then he has 20 gallons of water. How many gallons of water does he have at first?

The modern solution:

   x  -  3/8 x = 20        5/8 x = 20       x = 32

Egyptian " False Position" solution:

Try x = 8,    if originally Tom has 8 gallons of water

3/8 x = 3,   then he pours out 3 gallons of water

 8 - 3 = 5,     then he has 5 gallons of water. 

However, in the problem, Tom has 20 gallons of water left, which is 4 times as much  as 5 gallons of water. So this time, we could try 32 ( 4 x 8 = 32 ).

If x = 32,  3/8 x 32 = 12 , 32 - 12 = 20