# How to re-arrange the formula to make 'n' the subject

• September 7th 2009, 06:55 AM
danw76
How to re-arrange the formula to make 'n' the subject
Hello

How do I rearrange this formula to make 'N' the subject?

((1.86x£1-£1)xN)+((-£1)x(100-N)) = £7.88

I know that the parenthesis might not make complete sense, but this is a formula I am using in Microsoft Excel which works fine. At present I have values for 'N' which give me £7.88. There are other occasions where I have the £ value result, but do not know 'N'.

It's a long time since I have had to rearrange something like this. There are 2 N's which confuses me. Thanks in advance.

Dan Wright
• September 7th 2009, 07:07 AM
Aryth
For simplicity, I will exchange \$ for £

$((1.86\1 - \1)N) + ((-\1)(100 - N)) = \7.88$

$1.86(N)(\1) - N(\1) -100(\1) + N(\1) = \7.88$

Now we group all terms with an N in them:

$(1.86(N)(\1) - N(\1) + N(\1)) - 100(\1) = \7.88$

$1.86(N)(\1) - 100(\1) = \7.88$

$N(1.86(\1)) = \7.88 + 100(\1)$

$N = \frac{\7.88 + 100(\1)}{1.86(\1)}$

That's what I got, remember to switch the dollar sign for the euro sign. :P
• September 7th 2009, 08:54 AM
danw76
Thanks Aryth. That works great although I am finding it hard to understand how the the rearrangement rules work. I am also trying to re-arrange the formula to find 'T', but have not had any luck with that either.

Anyone have any ideas?

((Tx£1-£1)x58)+((-£1)x(100-58)) = £7.88