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china80 · Apr 21, 2013, 09:23 PM

Can you help me understand this equation and how did they arrive to the aswer of 300,000?

(X-0) X (1-36%) / 86,000 = (X-150,000) X (1-36%) /43,000

I know the result is 300,000, but I do not know how to get there.

ebaines · Apr 22, 2013, 06:27 AM

First - please be clear as to what symbols are what. I assume that you are using of the symbol 'X' for both an unknown and also the "times" symbol, which is very confusing. So please confirn that this is what you meant:

$ \frac {(x-0)(1-36%)} {86000} = \frac {(x-150000)(1-36%)}{43000} $

First note that 36% is equivalent to 0.36, so the (1-36%) portions of this equation are equivalent to (1-0.36) = 0.64.

$ \frac {(x-0)(0.64)} {86000} = \frac {(x-150000)(0.64)}{43000} $

Now note that the 0.64 term appears on both sides of the equation, so they cancel. Next, looking for common factors note that 86,000 = 2 times 43,000, so the two 43,000 terms also cancel and you have:

$ \frac {(x-0)\cancel{(0.64)}} {2 \times \cancel {43000}} = \frac {(x-150000)\cancel{(0.64)}}{\cancel {43000}} \\ \\ \frac {(x-0)} {2 } = {(x-150000)} \\ \\ \frac x 2 = x - 15000 $

Rearrange to get the 'x' term by itself on the right hand side, and move the 150000 term to the left hand side:

$ 15000 = x - \frac x 2 = \frac x 2 $

Now multiply both sides by 2:

$ 150,000 \times 2 = \frac x 2 \times 2 = x $

So $x = 2 \times 150000 = 300,000$

Hope this helps.