Fractional Algebra

[jdawg]

I have a rather basic applied algebra problem that I would love some help with as my high school level algebra has now totally eluded me
I have the basic financials of a company but this does not include sales
However, the DuPont ROE formula as below is:
Net income/Sales * Sales/Assets * Assets/Equity = ROE

I have all inputs except Sales.
So in algebra this would be solve S where we have values for all other inputs
N/S * S/A * A/E = R

So for example:
4/40 * 40/20 * 20/5 = 80%
But what I have is:
4/S * S/20 * 20/5 = 80%

What are the algebraic steps to solving S?
many thanks!

 

[skeeter]

4/S * S/20 * 20/5 = 80%

S can be any value other than zero ... maybe you can recheck the formula again?

 

[HallsofIvy]

I have a rather basic applied algebra problem that I would love some help with as my high school level algebra has now totally eluded me
I have the basic financials of a company but this does not include sales
However, the DuPont ROE formula as below is:
Net income/Sales * Sales/Assets * Assets/Equity = ROE

I have all inputs except Sales.
So in algebra this would be solve S where we have values for all other inputs
N/S * S/A * A/E = R

So for example:
4/40 * 40/20 * 20/5 = 80%
But what I have is:
4/S * S/20 * 20/5 = 80%

What are the algebraic steps to solving S?
many thanks!

Since "ab= ba" for any numbers, a and b, we can interchange numbers in the numerator with other numbers in the numerator, and similarly for the denominator, without changing the result.

So \(\displaystyle \frac{4}{S}*\frac{S}{20}*\frac{20}{5}= \frac{4*S*20}{S*20*5}= \frac{S}{S}*\frac{20}{20}*\frac{4}{5}\).

Of course, both \(\displaystyle \frac{20}{20}\) and \(\displaystyle \frac{S}{S}\) are 1 (as long as S is not 0) so that is the just \(\displaystyle \frac{4}{5}= 0.8= 80\)%.