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

1. ## 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

2. For simplicity, I will exchange $for £$\displaystyle ((1.86\$1 - \$1)N) + ((-\$1)(100 - N)) = \$7.88\displaystyle 1.86(N)(\$1) - N(\$1) -100(\$1) + N(\$1) = \$7.88$

Now we group all terms with an N in them:

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

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

That's what I got, remember to switch the dollar sign for the euro sign. :P

3. 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