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**BarandaMan****Guest**

Hey all!

I have two problems on the go, both of which I will continue to ask questions on (with all of your help!) until I understand, so thank you all.

This question: (i took a picture, put into address bar)

i50.tinypic.com/30bpftg.jpg

I have done the whole question and got the right results (the top two equations), but now I must solve them. I have no idea how to manipulate them to get the bottom results.

I think we expand both, then put one of them into the other, but I keep doing this wrong (I haven't seen this many terms before:P)... could we go through this please if someone can solve it?:P

**BarandaMan****Guest**

EDIT ^^

i48.tinypic.com/259ken7.jpg

I said in the above post 'top two equations', I meant middle two. Or the top two of the new (cropped) picture (link in this post).

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Hi;

I am looking at this link here:

i48.tinypic.com/259ken7.jpg

What do you want to do with that?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**BarandaMan****Guest**

bobbym wrote:

Hi;

I am looking at this link here:

i48.tinypic.com/259ken7.jpg

What do you want to do with that?

That's the right one!

Basically, using the top two equations on that page, to get the final answer somehow they have put one of them into the other and solved it, to give the two solutions below. I tried expanding both equations fully and substituting one into the other, but I cannot do it correctly. Does this make sense?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Hi;

You want to solve the first two simultaneously?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

**Online**

**BarandaMan****Guest**

bobbym wrote:

Hi;

You want to solve the first two simultaneously?

I am not entirely sure if I am honest (I mean the terminology, I am not sure if these are simultaneous equations?), but from thw two equations, we need to get an expression for qH and qL, which are contained within both equations.

If this is what you mean by simultaneously solving then I do mean that! Haha sorry I just don't want to use wrong terminology.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Hi;

Can you copy the entire question? Is it from a book? Surely there is more...

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

**Online**

**BarandaMan****Guest**

bobbym wrote:

Hi;

Can you copy the entire question? Is it from a book? Surely there is more...

This is after about 3 pages of derivations . This is simply it, I have links that I am using online which explain how to solve these.

They say because one of them is linear in the other two, they take an average figure for the other two, but I don't really undersatnd that method.

Why do you say that there must be more? Is three equations in three unknowns unsolvable?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

I see two equations, not three. I can solve them but I would like to be sure that is what is wanted before I do.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**BarandaMan****Guest**

bobbym wrote:

I see two equations, not three. I can solve them but I would like to be sure that is what is wanted before I do.

Apologies! I thought you posted the last response in my other topic!

There is two questions in two unknowns, I can show you the answer in the book if you want?

It skips out how to do it because we (should ) be able to the algebra as that wasn't the focus of the question, but as always it trips me up!

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Hi;

I am seeing at least six unknowns in those two equations. Which two do you want solved for?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**BarandaMan****Guest**

bobbym wrote:

Hi;

I am seeing at least six unknowns in those two equations. Which two do you want solved for?

Hello bobbym, apologies for delayed reply. Internet going. It's 3am now!

Need to solve just for qh and ql! The solutions are at the bottom of the picture if you want to check!

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Okay, you want to check their answer?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**BarandaMan****Guest**

bobbym wrote:

Okay, you want to check their answer?

No no! I am just letting you know, so you can see and check your result I guess, sorry.

I tried expanding their answer and working backwords and couldn't do it. Basically we need to get from the two expressions, expressions for qh and ql as seen in the answer (the bottom two lines), but I cannot do it. That is what I am trying to do!

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Ypu want to work from their answer to where?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**BarandaMan****Guest**

bobbym wrote:

Ypu want to work from their answer to where?

No where, I want to know how they found the answer. I cannot get it. I did all the work to get to the top two equations in the second link I posted. From then we are meant to 'rearrange/substitute etc' and get expressions for qH and qL (as shown by the bottom two equations, i.e. the official answers). I cannot rearrange/substitute the top two equations to get to those given in the answer book. This is what I am looking for help on, if you can solve this please can you show me how?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

I can not guarantee anything here. I will look at it and post if I get something.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**BarandaMan****Guest**

bobbym wrote:

I can not guarantee anything here. I will look at it and post if I get something.

Ok thank you!!! if my objective with this is unclear please ask and i will try and be more direct.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Hi;

First answer is correct. So is the second one.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**BarandaMan****Guest**

bobbym wrote:

Hi;

First answer is correct. So is the second one.

OH MY LORD you are INCREDIBLE! You teach me on any topic I need help with and you can just solve these kinds of things?!

Could you please please post a solution for this? I know you must hate me asking for a full solution, but this is just one where i need to see how someone did it / thought about it!

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

I didn't get a solution to it. Just because you see an answer in a book that does not mean the author worked it out.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**BarandaMan****Guest**

bobbym wrote:

I didn't get a solution to it. Just because you see an answer in a book that does not mean the author worked it out.

But were you able to rearrange/substitute the top two equations to get the same expressions as those posted?

It is not the answer, but that is what I cannot do, I cannot rearrange them. I really want to do it...please help me? Does it make sense?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

First I must ask a question:

If you saw this in a book,

would you ask someone how they did it by hand?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**BarandaMan****Guest**

bobbym wrote:

First I must ask a question:

If you saw this in a book,

would you ask someone how they did it by hand?

No of course not! I would use a calculator!

But do you see what I mean? It is not the solution, but I am really bad at substituting/manipulating the formulas in the way required, so this is a real chance for me to see the method used. There was a lot before that step to get to those two equations, then the 'answer' is to express them in terms of qh and ql. However, I cannot do that and really need help. Will you not help me? I just cannot rearrange/manipulate.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Same thing here, we both used a computer but I will show you how you might do it by hand.

Start by expanding the 2 equations,

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**