formual manipulation

[account39]

I still don't have a formula for that works.

I need a formula to solve for 'a', given the formula

w = 100 / { [ ( 0.95a + 20.9) - 12 ] / c } + 1

I don't know how to do this sort of thing, I don't have a teacher, I'm an old guy & have forgotten most of the math I learned,
if you could help me, it would be appreciated.

thank you

ps Is there no way to delete my posts, or is it automatic after a certain period of time?

 

[mmm4444bot]

My head starts feeling stuffy, when I look at things like (((( .

To me, it appears that some of those grouping symbols are not needed.

Is the following correct?

\(\displaystyle w \;=\; \frac{1}{\frac{0.95a \;+\; 20.9 \;-\; 12}{2} \;+\; 1} \cdot 100\)

If so, then we can subtract 12 from 20.9 right away.

\(\displaystyle w \;=\; \frac{1}{\frac{0.95a \;+\; 8.9}{2} \;+\; 1} \cdot 100\)

Both of the terms 0.95a and 8.9 are being divided by 2. Let's do those divisions.

\(\displaystyle w \;=\; \frac{1}{0.475a \;+\; 4.45 \;+\; 1} \cdot 100\)

We can combine the constants 4.45 and 1.

\(\displaystyle w \;=\; \frac{1}{0.475a \;+\; 5.45} \cdot 100\)

The multiplication by 100 occurs in the numerator.

\(\displaystyle w \;=\; \frac{100}{0.475a \;+\; 5.45}\)

Okay. At this point, I'm uncertain as to whether or not you're asking how to solve for a. It seems not, so I'll just post my result for a.

\(\displaystyle a \;=\; \frac{\frac{100}{w} \;-\; 5.45}{0.475}\)

If we divide both terms in the numerator by 0.475, and round to eight places, we get the following.

\(\displaystyle a \;=\; \frac{210.52631579}{w} \;-\; 11.47368421\)

Let us know, if (at the onset) I misinterpreted your nested grouping symbols.

 

[mmm4444bot]

You replaced 2 with c, while I was typing my post. (Heh, heh.)

Now we have the following.

\(\displaystyle a \;=\; \frac{105.26315789 \cdot c}{w} \;-\; 1.05263158 \cdot c \;-\; 9.36842105\)

 

[Denis]

I need a formula to solve for a, given the formula
w = 1 / ( ( ( ( 0.95a + 20.9 ) - 12 ) / c ) + 1 ) x 100

Do not use "x" for multiplication (looks like a variable); use *

There is NO "formula" to solve for a: you simply solve for a .
(the way Mark showed you)

You can ease the work with "tricks" like: let k = .95a + 20.9
And since a final multiplication by 100 is made, show it in numerator; like:
w = 100 / (((k - 12) / c) + 1) : don't look as scary as originally, right?

Now solve that for k, then for a.

See if you can get to: w = 100c / (k + c - 12)

If not, then you need help from your teacher.