False Position HW Question

 Egyptian Problem:

 

Twice the quantity and its fifth, added together, give 22. What is the quantity?

 

Modern solution:

 

2x + x/5 = 22,    


11/5x = 22 , x=10


 

Egyptian “False Position”

 

Try x=5

 

2x + x/5= 10 + 1 = 11

 

We need 22, which is twice as big. So x must be twice as big as the trial number.

 

5 * 2 = 10

 

 

Check: if x=10, 2x + x/5 = 20 + 10/5 = 20 + 2 = 22

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