A formula for 3 unknowns?

In 2010, it's 'File / Options / Add-ins / Manage Excel Add-ins', button 'Go...': check 'Solver Add-in'
Then you can find it in the ribbon 'Data / Analysis' (on the far right)
eric

With Babar's remark, I realize something:
the screenshot in the file is not correct, it has evolved. Read $G$2 in the cell to be defined.

Eric

Just for info,

You can directly call (and configure) the solver via macro (or function) with the code:

Sub Solver()
'In the VisualBasic Tools/References menu, check the SOLVER box
'Look at the SOLVER Help
SolverOk SetCell:="$G$2", MaxMinVal:=3, ValueOf:="0", ByChange:="$B$3:$D$3"
SolverSolve
End Sub

See also, of course, SOLVERADD to add/modify constraints (detailed example at the bottom of the page).

Hello,

they do not appear as reel numbers but as decimals
I suppose read 'as integers'.
Without an example file, it's hard to see anything.

eric

Re,

But what is it that doesn’t suit you about the solution that Eriiic is proposing to use the Excel solver?
Especially since you can DIRECTLY call it and configure it via macro, without having to deal with a complex script?

See you!

Good evening,

Here is an xlsm file that, in my opinion, does the job.
https://www.cjoint.com/c/CFExoncKufQ

However, please note that for 500,000 solution triplets, it takes several minutes to process.

Best regards

Note: with (a, b, c) = (1, 1, 1) and Total = 1,000, we get 501,501 solutions.

Absolutely perfect, it's exactly what I needed! :D
But since I use results with quite small values, there are never a lot of possible solutions, always one or two at most!

Thank you anyway for your answers!

Hello michel_m

You are talking about a linear system of 3 equations with 3 unknowns.

This is a linear equation with 3 unknowns and 3 explicit constraints (the unknowns are natural integers) and 3 implicit constraints (a<=ent(total/prix_A), b<=ent(total/prix_B), c<=ent(total/prix_C)),

That is why I proposed a "jackhammer" macro that tests all possible combinations of integer triplets (a,b,c) within the constraint ranges [0, ent(total/prix_A)] x [0, ent(total/prix_B)] x [0, ent(total/prix_C)].

As for the national education system, I don't recall any exclusion of matrix calculations.
In my time, it started in the 10th grade, gently progressing until the final year; it became "abstract" linear algebra until the bachelor's degree and made sense as it became "applied" everywhere afterwards.
As for now, I don't know.

Best regards

Hello

a good explanation in an xls file is really coooooool thank you Michel :)

Hello,

To Jvdo:
I'm far from being young and I had never heard of matrix calculation until the math info course at Cnam with error detection codes; in fact, the entire audience was discovering them too

Have a good evening :o)