Hi,
I read this
X/1294 = (14851 + X) / 15604
=>
X = 1294 * 14851/ (15604 - 1294)
I can't see how this is done, is it correct ?
If I multiply through by 1294 I get
X = (1294 *14851/15604) + (1294 * X / 15604)
and I don't see how the right hand side can simplify into the above expression.
so can you teach me how this works (I reckon this has been troubling me for at least 40 years)
Adrian Thanks.
I replied in detail with my working but the post was lost
Basically
X/1294 = (14851 + X) / 15604
X/a = (b+x)/ c
X = ab/c + ax/c
X - ax/c = ab/c
X*(1- a/c) = ab/c
1- (a/c) = (c-a)/c
X= (ab/c) / (c-a)/c
or even
x = ab/c *c/c-a
X = ab/c-a
Ok so I've managed it - is this a generic transformation, is there a rule, or do I have to do the algebra each time ....
X = 1294 * 14851/ (15604 - 1294)
X = ab/c - a
Your general formula appears to be correct. I would not memorize it. Know the rules of algebra and apply them each time. Once you're very comfortable with the rules of algebra, and only then, I would probably use a CAS to solve it.