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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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

$x = 180$ $x=180$

Explanation:

Let the quantity of barley be $x$ $x$ . As $\frac{2}{3}$ $2/3$ of $\frac{2}{3}$ $2/3$ of this is taken and $100$ $100$ units added to it, it is equivalent to

$\frac{2}{3} \times \frac{2}{3} \times x + 100$ $2/3xx2/3xx x+100$

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

$\frac{2}{3} \times \frac{2}{3} \times x + 100 = x$ $2/3xx2/3xx x+100=x$ or

$\frac{4}{9} x + 100 = x$ $4/9x+100=x$ or

$\frac{4}{9} x - \frac{4}{9} x + 100 = x - \frac{4}{9} x$ $4/9x-4/9x+100=x-4/9x$ 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.

$x=180$

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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...

1 Answer

Explanation:

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