Solving an equation (sorry, maths not science)

[MrPahoehoe]

Hi. I was doing a percentage calculation (not really important) and was trying to work out how much of an additional substance on top of a known value, would equal 17% of the total. The formula below is how i first tried to work it out. I know there are easier ways of doing this (I've since worked it out another way), but completely failed in trying to re-arrange this really simple equation. I don't need the answer - I now know its about 12.55, but would really like someone to explain how to re-arrange/solve this equation....

17% = 100 * x / (x+61.3)

Also, please can you have a step-by-step solution and show your working because I'm not awesome at this....

Cheers, MrP

Incidentally, this is how i tried to solve it:
(* 100) 0.17 = x / (x+61.3)
(* (x+61.2)) 0.17x + 10.421 = x/x + x/61.3
0.17x + 10.421 = 1 + x/61.3
Pretty sure I've gone wrong somewhere here, because this doesn't work

[jake-the-peg]

OK so 17% is 0.17

0.17=100* x/(x+61.3) - multiply both sides by (x+61.3)
0.17(x+61.3) =100x - multiply to get rid of the brackets
0.17x+61.3 *0.17 =100x -subtract 0.17x from both sides and multiply 61.3 by 0.17
10.421=99.83x - divide both sides by 99.83
x=10.421/99.83
x=0.1043

Not sure abiout your logic but that's how you'd do the algebra

[jake-the-peg]

I think what you're trying to achieve is to answer a question like a book costs £10 including vat if VAT is 17% how much is VAT?

In that case

X(price) *1.17 = £10
X=10/1.17 = £8.54 = price before VAT

8.54 * 0.17 = VAT = £1.45

Check: £1.45 + £8.54 = £9.99 ( rounding issue)

Does that help at all?

[vascop]

Jake
I think you got it wrong. Mr POahowhoe has multiplied the right hand side by 100 so you must keep the 17 as 17!!
So
Multiplying both sides by (x+61.3) gives:
100x=17(x+61.3)
100x=17x+17 times 61.3
Subtracting 17x from both sides gives:
83x=17 times 61.3
Dividing both sides by 83 gives:
x=17 times 61.3/83
x=12.55

[jake-the-peg]

Well he's used 0.17 in his workings - perhaps that's where he wen't wrong

[rov1200]

If Jake is right about your problem revolving about VAT you have to be careful.

I was once given a bill for car repairs and he gave the TOTAL bill as £117.50. He then proceeded to work out the VAT and took 17.5% of £117.50 which is wrong.

The reason is you get a different VAT if you take the bill to be £100 + VAT =£117.50 although this final figure is the same.

This is the major cause of error for the VAT man.