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Hi all,
I am in a bit of a pickle with a math problem and figured you guys were the best to ask for advice.

I have to transpose a formula to make a variable the subject.

This was simple enough for one of the variables, however the second has me absolutely stumped.

My maths brain is not a strong one so I would like some help.

This is homework so I do not want the actual answer. I need to solve it, I would like some clarity on the process that is tripping me up.

the formula is


D = ((F-S)/S)*100



I found F easily enough by working in reverse

first D/100
then multiply by S
then add S

So I ended up with

F=((D/100)*S)+S

The hard one for me is finding S.

It just turns my brain insideout.

The methode I used for the first transposition doesnt seem to make sense here.

so I try the balancing the = sign method to be left with s on one side.

D/100 = (F-S)/S
...
then I can't think of how to go any further as S is taken from F and the result is devided by S I can't think of how to get F across the
other side.

Like I said, I really struggle with this stuff and so maybe explaining my process will allow you to see where I am mixing myself up.

Any hints, rules, rymes or web links to simplified explanations would be greatly appreciated.

even examples using what I need to do with a different formula -if that doesn't give away the answer to easily.

Kezzla

D/100 = (F-S)/S

DS/100 = F-S

(DS/100) - F + S = 0

DS - 100F + 100S = 0

You need to know the values of D and F and then solve using quadratic formula. (Or another method for solving quadratics)

EDIT: Lol this isn't even a quadratic, good job I don't do maths anymore.

This is probably the most laughably roundabout way to do it, but here goes:

We know this is F:



Subtract S from both sides:



Divide both sides by S:



Change the division by S into a multiplication by 1 over S:



Distribute 1 over S:



S over S simplifies to 1:



Add 1 to both sides:



Multiply both sides by S: (hey look, we're back to F, but a different form)



Divide both sides by ((D/100)+1):



Throw a party:



Note: Distribute to simplify that answer

It took me three tries but I think I got it. I replaced 100 with 'a' to make it simpler.
I will use underline to group terms where it can be used unambiguously. (I hate brackets {and irony}).

1. d = (f-s)/s*a

2. d = (f-s)a/s

3. d = af-as/s

4. d = af/s - as/s

5. d = af/s - a

6. a+d = af/s

7. 1/s = a+d/af

8. s = af/a+d

This thread is painful to read. In an early post you already have:



which simply means




since S is a common factor on the RHS.

That in turn means that



Edit: which could of course be written more simply.

Thanks for your help guys, I need to practice this stuff a lot before I am going to do this without my head breaking, I think GG's one I could see clearest.

I know it's not the point, but I tried to brute force it using a spreadsheet. I was hoping to start with the correct answer and work back to one of the other inversions. I can see from your examples there are numerous ways to rework the formula to find S, which is interesting in itself.

The answer I ended up with was,

S= (F*100)/(D-100)

That certainly correctly gives S. But I have no idea how.

My course trainer is coming around on friday, I think we will have to have a maths day.