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Counting equations with two parallel counters

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First of all, a bit of introduction in order to avoid the XY problem: when I write a test/exams I like to keep text and solution together. Now, both the main text and the solution can have equations; I'd like that the equation numbering of the main text could be kept constant, both in the formulation-only document and the full one (formulation with the solution).

I am able to do it for figures (I use newfloat to define a solfigure environment which has labels like Figure S1 and so on), but I am at a loss thinking something similar with equation.

I prepared this MWE:

\documentclass{article}\usepackage[T1]{fontenc}\usepackage[utf8]{inputenc}\usepackage{xcolor}\usepackage{environ}\newif\ifsolution\solutiontrue\NewEnviron{solution}{\ifsolution\color{red}\expandafter\BODY\fi}\begin{document}\begin{equation}    2x=4    \label{eq:one}\end{equation}\begin{solution}    \begin{equation}        x=2        \label{eq:solone}    \end{equation}\end{solution}\begin{equation}    3x=6    \label{eq:two}\end{equation}\end{document}

With \solutiontfalse I have equation (1), (2); with \solutiontrue I have (1), (2), (3); I'd like to have (1), (S1), (2)... and so on, so that the equation for (2) is the same one both in the formulation and the formulation+solution document.

Extra point for having the tag in red, too.

With \solutionfalse:

output for the formulation

With \solutiontrue:

output for the formulation + solution


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