Math Is Fun Forum

nadbconvteam

Guest

Re-arrange Margin Formula

Okay, so i am trying to teach my sales team basic maths such as how to work out or add markup/margin, profit etc.  I am trying to show how to re-arrange the margin formula so they can add margin to a cost price, I've got the steps below which I think are correct but don't know how to explain step 6.  Can someone please confirm this is correct and what is happening in step 6?

??????=(???? ????? −???? ?????)/(???? ?????)
(???? ????? −???? ?????)/(???? ?????)=??????
???? ????? −???? ?????=?????? ×???? ?????
???? ?????−???? ????? −?????? ×???? ?????=0
???? ????? −?????? ×???? ?????=???? ?????
(−??????+1)×???? ?????=???? ?????
???? ?????=(???? ?????)/(−??????+1)

nabdconvteam

Member

Registered: 2022-03-03

Posts: 3

Re: Re-arrange Margin Formula

Margin=SalePrice-CostPrice/SalePrice
SalePrice-CostPrice/SalePrice=Margin
SalePrice-CostPrice=Margin*SalePrice
SalePrice-CostPrice-Margin*SalePrice=0
SalePrice-Margin*SalePrice=Cost Price
(-Margin+1)*SalePrice=Cost Price
SalePrice=CostPrice/-Margin+1

Sorry, don't know why the original post formate was wrong!  Hope the above makes sense couldn't figure out how to post an image.

Last edited by nabdconvteam (2022-03-03 23:05:32)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Re-arrange Margin Formula

hi nabdconvteam

Welcome to the forum.

My apologies for the late reply.  I've only just spotted your post. To simplify I'm just going to use M, S, and C here.

I think your starting point is

If you cannot write that without using / for divide then you need to include a bracket thus:

M = (S-C)/S

The re-arrangement follows these steps:

Step 1. remove the fraction by multiplying both sides by S

Step 2. Move all the S containing terms together by adding C to both sides and subtracting MS from both sides.

Step 3. The RHS has a common factor S so it can be factorised outside a bracket.

Step 4. Finally you can divide both sides by the bracket (1 - M)

Usually we would then switch around the LHS and the RHS to make S the subject of the formula.

Hope that helps.

I am teaching another member how to change formulas around here http://www.mathisfunforum.com/viewtopic.php?id=27132

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nabdconvteam

Member

Registered: 2022-03-03

Posts: 3

Re: Re-arrange Margin Formula

Thanks so much for your help Bob.  It was the factoring that I didn't get, will read up.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Re-arrange Margin Formula

The step S - SM = S(1-M) is one that sometimes catches people out.

For S to be a common factor of both terms there has to be a second factor that gets 'left behind' in the bracket.  The first term just has S so what is the other factor?

You cannot just leave a hole eg. S(    - M)

You need to realise that S = 1 times S so the other factor is a 1, hence S ( 1 - M)

The Math Is Fun pages on factoring get hard pretty quickly.  Here's a good U Tube video that starts with easier stuff:

https://www.youtube.com/watch?v=-VKAYqzRp4o

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob