Bob

]]>Why so many answers to this? :

an expression for 'e', without using 'e','r', or 'a*'....

Well there is a good reason why this happened.

There are 4 equations and 12 variables. For the first part you were asked to get one equation with 3 variables forbidden. It worked like this:

4 equations and 12 variables ... eliminate e gives

3 equations and 11 variables ... eliminate r gives

2 equations and 10 variables ... eliminate a* gives

1 equation and 9 variables.

So we have lost the three variables exactly as required. There's only one answer. (with maybe a bit of re-arranging)

For part two you are asked for one equation with two variables forbidden ( 'e' doesn't count because that's the one we are trying to make)

4 equations and 12 variables ... eliminate 'r'

3 equations and 11 variables ... eliminate a*

2 equations and 10 variables.

We've eliminated the forbidden variables but still have two equations. You can still eliminate a variable if you want and get a correct equation. But which one to eliminate? There's lots of choices so lots of answers. Your teacher is going to have lots of work checking each different answer to see if it works. Unless the question is worded in such a way that it steers you towards one answer rather than another.

Bob

]]>Oh yes. I had an expression for alpha e too and made the same mistake!

Now you see the value of the number values trick. Not only did it tell you there was a mistake; but it also helped you to spot what it was.

Bob

It is incredible, thank you so much for this. I will definitely try create my own in the future for similar problems to check my work!

]]>my other solution for e, which I hope is what you got, is:

e= ((alpha*A) + g* - ((b* + gammaA - b)/gamma)) / alpha (the whole thing over alpha)

]]>Now you see the value of the number values trick. Not only did it tell you there was a mistake; but it also helped you to spot what it was.

Bob

]]>I get it to equal 6 funnily enough, not 3 xD!

I didn't have the WHOLE expression over alpha (which =2), I left that out by mistake, sorry! So it does in fact equal 3! Yay!

]]>hi

If you mean this:

then it works with numbers, so I think it is ok. I got a different expression because I kept in alpha g and gstar but not gamma and b.

Bob

Oh no, for 'a' i am getting the trick correct in excel.

But with 'e' as above, the numbers aren't equalling e=3 as they should? Do you get this too?

]]>I'll await your answers. Doing nothing is easy!

Bob

ps. the spreadsheet trick 'works' because the rules of algebra are just the rules of arithmetic. So, if it doesn't work with numbers, then the algebra must be wrong.

]]>Oh yes. You might find the following helpful in checking your algebra.

I used a spreadsheet to substitute numbers into the equations.

First I entered the 12 variable names in a row.

Then I chose numbers for those that occur in equation 1 and made a formula to calculate 'a'.

Then I constructed the equation for astar. Of course I'd already fixed the value but I hadn't chosen a value for gstar yet. So I just fiddled the value of gstar so that astar came out correctly.

Then I made the equations for b and bstar.

So that gave me 12 variables with values consistent with the 4 equations.

When I had finished my equation for a, I evaluated it using that formula and my chosen variables. You can see in my screen shot below that it evaluated to 51 as required. And I checked yours and it too gave 51.

Now that trick is not 100% foolproof. You could have errors that 'cancel out' leaving an answer that looks correct when it isn't. But it's very unlikely with those numbers, so I was pretty confident we were both using correct formulas.

I saved the spreadsheet, so when you offered an equation for 'e', all I had to do was construct the equation in the spreadsheet and look to see if e came out correctly.. It did!

Bob

This is absolutely incredible. Thank you so much. I should now be able to tackle the third part of the question. This has all been really helpful.

I will try not to derive the expression for 'e' with alpha g and g* to see if I can do it, I love this kind of substitution when it goes correct!

Thank you! When I have an expression with g* and g, I will post it here and if you could maybe let me know if it is what you had, that would be great! Please don't post it before hand, I really want to see if i can do this hahaha!

Thank you Bob!!!

I used a spreadsheet to substitute numbers into the equations.

First I entered the 12 variable names in a row.

Then I chose numbers for those that occur in equation 1 and made a formula to calculate 'a'.

Then I constructed the equation for astar. Of course I'd already fixed the value of astar but I hadn't chosen the value for gstar yet. So I just fiddled the value of gstar so that astar came out correctly.

Then I made the equations for b and bstar.

So that gave me 12 variables with values consistent with the 4 equations.

When I had finished my equation for a, I evaluated it using that formula and my chosen variables. You can see in my screen shot below that it evaluated to 51 as required. And I checked yours and it too gave 51.

Now that trick is not 100% foolproof. You could have errors that 'cancel out' leaving an answer that looks correct when it isn't. But it's very unlikely with those numbers, so I was pretty confident we were both using correct formulas.

I saved the spreadsheet, so when you offered an equation for 'e', all I had to do was construct the equation in the spreadsheet and look to see if e came out correctly.. It did!

Bob

]]>If you mean this:

then it works with numbers, so I think it is ok. I got a different expression because I kept in alpha g and gstar but not gamma and b.

Bob

]]>hi BarandaMan,

e=A - (theta(b*+gamma(A)-b))/gamma - g

Where did theta come from?

and did you mean

So I have checked this

and it doesn't work out when I substitute numbers.

I'll have a go and see what I get.

Bob

Yes sorry, I meant phi, I need to revise the Greek alphabet

But I got :

Really appreciate the help. Your method for the a expression is brilliantly intuitive and I have written that out in full. Thank you.

]]>