solve S = p / (q + p)(1 - q) for q

[jenjen2]

Hi. I've been working on this, and I can't figure out what I'm doing wrong. I solved all the other problems in this workbook section with only minor issues, but I got completely stuck on this! I know the answer, but I can't seem to get there!

The problem is:

S = p / (q+p)(1-q) ; solve for q

The answer at the back of the book is:

q = p(1-S) / s(1-p)

And here's my closest-to-correct work:

S = p / q+p)(1-q)
p/S = (q+p)(1-q)
p/S = q - q^2 + p - pq
p/S - p = q - q^2 - pq
p/S - p(S/S) = q - q^2 - pq
p - pS / S = q - q^2 - pq
p - pS = S(q - q^2 - pq)
p(1-S) = Sq (1 - q - p)
p(1-S) / S(1 - q - p) = q
(flip sides)
q = p(1-S) / S(1-q-p)

So I end up with an extra (-q) on the right side of the equation. I know where the extra (-q) comes from, but I can't see any way around it. Thanks in advance for your help!

Jen
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[Denis]

"p/S = q - q^2 + p - pq"
At this point, go this way:
q^2 + pq - q - p + p/S = 0
q^2 + q(p - 1) - p + p/S = 0

Now call in ye olde quadratic :wink:

 

[jenjen2]

A big thanks to Denis!!

I'll keep working on it with the quadratic formula and tell y'all what I come up with. For the last hour, I've been working in circles with the q.f. on this.
But I will keep going until I get it (or it gets me).

Stay tuned...

Jen

 

[jenjen2]

Still need help, please!

[insert screams of agony here]

I still can't get it. The quadratic formula isn't helping me - I don't understand it and and I haven't even gotten to the QF section yet in my book! I'm embarrassed to admit that I've spent more than four hours on this problem - I really need some additional step-by-step help if anyone is available and willing.

Thanks again,
Jen

 

[Denis]

The problem is:
S = p / (q+p)(1-q) ; solve for q
The answer at the back of the book is:
q = p(1-S) / s(1-p)

Well Jen, you can keep trying till you're blue in the face...you'll NEVER get that answer!

It is the answer to:
S = p / [p(1 - q) + q]

p(1 - q) + q is NOT equal to (q + p)(1 - q).

So there's a typo either in the question or in the answer :shock:

But I must say: ya sure got tenacity :wink:

 

[jenjen2]

Thanks so much, Denis. You saved the day.