Suppose, 2/3 of 2/3 of a certain quantity of barley is taken, 100 units of barley are added and the original quantity recovered. find the quantity of barley? This is a real question from the Babylonian, posited 4 millenia ago...

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Answer 1 · 2016-09-12T03:53:23

#x=180#

Let the quantity of barley be #x#. As #2/3# of #2/3# of this is taken and #100# units added to it, it is equivalent to

#2/3xx2/3xx x+100#

It is mentioned that this is equal to the original quantity, hence

#2/3xx2/3xx x+100=x# or

#4/9x+100=x# or

#4/9x-4/9x+100=x-4/9x# or

#cancel(4/9x)-cancel(4/9x)+100=x-4/9x=9/9x-4/9x=(9-4)/9x=5/9x# or

#5/9x=100# or

#9/5xx5/9x=9/5xx100# or

#cancel9/cancel5xxcancel5/cancel9x=9/5xx100=9/cancel5xx20cancel(100)=180# i.e.

#x=180#