revaxarts said

http://www.wolframalpha.com/input/?i=Y+%2B+%28Y+*+A%2F100%29+%2B+%28Y+*+B%2F100%29+%2B+%28Y+*+C%2F100%29+%3D+D&x=0&y=0

mind blown, that service is epic!

and finally (I don’t know how to write this *incrementally* one out mathematically???)

Y would be 6 in the below:

Y + 14% + 13% + 9% = 8.424828

eg: 6 + 14% = 6.84 6.84 + 13% = 7.7292 7.7292 + 9% = 8.424828

Would it be possible to solve Y when things are calculated incrementally like that?

edit, I guess you do it step by step in reverse, rather than a single calculation (I think that is where I was getting stuck in the beginning)

8.424828 / 1.09 = 7.7292 7.7292 / 1.13 = 6.84 6.84 / 1.14 = 6

All these examples use the Distributive property of addition. When you have A, B, C you can easily get A/100, B/100, C/100 in real number (a, b, c). Then just apply this:

Y*a + Y*b + Y*c = Y* (a + b + c) = d (d as another real number) Y = d / (a + b + c)

As **gbs** mentioned, it would be just the same:

$y = $d/(1+0.01*($p1+$p2+$p3));

where p1, p2, p3 – any percents you like.

Does anybody is using paper and pencil except me?

Y + (Y * 10/100) + (Y * 10/100) + (Y * 10/100) = 3.9 means : Y + Y * 0.3 = 3.9 Y * 1 + Y * 0.3 = 3.9 Y * 1.3 = 3.9 Y = 3.9 / 1.3

dtbaker said

and finally (I don’t know how to write thisincrementallyone out mathematically???)Y would be 6 in the below:

Y + 14% + 13% + 9% = 8.424828eg: 6 + 14% = 6.84 6.84 + 13% = 7.7292 7.7292 + 9% = 8.424828Would it be possible to solve Y when things are calculated incrementally like that?

edit, I guess you do it step by step in reverse, rather than a single calculation (I think that is where I was getting stuck in the beginning)

8.424828 / 1.09 = 7.7292 7.7292 / 1.13 = 6.84 6.84 / 1.14 = 6

Hi, so you want to have the percents from the intermediate results from the calculation befor.

We could write it out like this:

Y + a*Y + b*(1+a)*Y + c*(1 + b)**(1 + a)*Y = d

If we go on:

Y + aY + bY + abY + cY + acY + bcY + abcY = d

Then we take Y out:

Y * (1 + a + b + ab + c + ac + bc + abc) = d Y = d/(1 + a + b + c + a*b + b*c + a*c + a*b*c)

In the above example, a, b and c are not written as percent, but as real numbers, i.e. in your example: a = 0.14, b = 0.13, c = 0.09

Your d is 8.424828.

Let’s checkif everything works by putting these values in the formula:

Y = 8.424828 / (1 + 0.14 + 0.13 + 0.09 + 0.14*0.13 + 0.13*0.09 + 0.14*0.09 + 0.14*0.13*0.09)

If we do the multiplications first we end up with:

Y = 8.424828 / (1 + 0.14 + 0.13 + 0.09 + 0.0182 + 0.0117 + 0.0126 + 0.001638)

Addition:

Y = 8.424828 / 1,404138 = 6

Tada

So, to make it quick, this is the formula you need with a,b,c written as real numbers:

Y = d/(1 + a + b + c + a*b + b*c + a*c + a*b*c)

Creattive said

So, to make it quick, this is the formula you need with a,b,c written as real numbers:Y = d/(1 + a + b + c + a*b + b*c + a*c + a*b*c)

awesome sauce!

Not that it was hard, but, I forgot math for a while

I’ll get back to you. Good night.