Maths problem

[bulb763]

Hoping to draw on some of the maths experts knowledge that I've seen lurk on here

I know St.
I know B1, B2, B3, B4... Bn (where B1>B2>B3>B4>Bn)

I want to split St up into S1, S2, S3, S4... Sn (where S1<S2<S3<S4<Sn), so that the Sum of S1 to Sn = St. But also,
S1*B1 = S2*B2
= S3*B3
= S4*B4
= Sn*Bn
= W

So basically, I am trying to work out how to work out the values of S1, S2 etc so that S1*B1, S2*B2 etc always equals W. I can see that there is a relationship in there somewhere and that I have all the information required, so I know it can be expressed as an equation, I just cant see how I'd like to express S1, S2, etc in terms of St and any/all of the B's, IYSWIM

Use these values as an example

St = 1000

B1 = 12
B2 = 6.5
B3 = 3.25
B4 = 2.75

S1 = ?
S2 = ?
S3 = ?
S4 = ?

W = whatever (this doesn't matter, but I suspect that there is only one value that will work)

Ultimately I want to use the formula in Excel. Maybe simultaneous equations would work but I'm not sure I'd be able to use those in Excel :shrug:

Over to you...

Edited by bulb763 on Monday 11th August 17:01

[Simpo Two]

Honolulu?

[arun1uk]

Control+Alt+Delete

Edited by arun1uk on Monday 11th August 17:02

[mercemployee]

THe answer is almost certainly 42

[Technonotice]

mx5?

[smutbag]

mercemployee said:

THe answer is almost certainly 42

[batfink79]

w = 3


HTH

[gti-ted]

AK47

[john_r]

Meh...

[N1CK]

ahh i see im not the only one that got two F grades in maths then

[SS HSV]

Pie = 3.14215936 is a round thing you eat.

Well this is a motoring website after all

[ludo]

I think S1 = St*B1/(B1 + B2 + B3 + ... + Bn)

you can then work out the rest by e.g. S2 = S1*B1/B2, S3 = S2*B2/B3 etc

but I haven't been bothered to check. Out of interest, what is the underlying problem?

[Neil_H]

Thursday.

[Justayellowbadge]

Can't have that, Mr H. Here you go, have one on me.

[ludo]

ludo said:

I think S1 = St*B1/(B1 + B2 + B3 + ... + Bn)

you can then work out the rest by e.g. S2 = S1*B1/B2, S3 = S2*B2/B3 etc

but I haven't been bothered to check. Out of interest, what is the underlying problem?

Oops, shouldn't have tried to solve it in my head, having checked it, I think it should be

S1 = St*B1/(1/B1 + 1/B2 + ... 1/Bn)

or more generally

Si = St*Bi/(1/B1 + 1/B2 + ... + 1/Bn)

having said which, my maths isn't usually that much more reliable with pen and paper

[fleetelise]

just whack it in excel with three columns.

column 1 = B
column 2 = S
column 3 = W

enter known Bs
enter formula for S
enter formula for W

have S1 set as 1

set one cell to be the summation of all the esses. Now, use the solver to set the summation of the esses to your desired value by altering S1, the answer should drop out.

[ludo]

ludo said:

ludo said:

I think S1 = St*B1/(B1 + B2 + B3 + ... + Bn)

you can then work out the rest by e.g. S2 = S1*B1/B2, S3 = S2*B2/B3 etc

but I haven't been bothered to check. Out of interest, what is the underlying problem?

Oops, shouldn't have tried to solve it in my head, having checked it, I think it should be

S1 = St*B1/(1/B1 + 1/B2 + ... 1/Bn)

or more generally

Si = St*Bi/(1/B1 + 1/B2 + ... + 1/Bn)

having said which, my maths isn't usually that much more reliable with pen and paper

yep, wrong again:

S1 = St/(B1*(1/B1 + 1/B2 + ... 1/Bn))

or more generally

Si = St/(Bi*(1/B1 + 1/B2 + ... + 1/Bn))

for the example I get

S1 = 91.7225
S2 = 169.3393
S3 = 338.6786
S4 = 400.2566

W = 1100.7056 (ish)

I think I've got it right now

[fleetelise]

using my "solver" method


B S W
1 12 91.72546513 1100.705582
2 6.5 169.3393202 1100.705582
3 3.25 338.6786405 1100.705582
4 2.75 400.2565751 1100.705582

[ludo]

fleetelise said:

using my "solver" method


B S W
1 12 91.72546513 1100.705582
2 6.5 169.3393202 1100.705582
3 3.25 338.6786405 1100.705582
4 2.75 400.2565751 1100.705582

reassuring! Elise ownership is obviously a sign of intelligence

[boobles]

Isnt S1 & S2 an Elise?