Your rich uncle died, leaving you with 40 atoms of carbon and 150 atoms of hydro

Question

Your rich uncle died, leaving you with 40 atoms of carbon and 150 atoms of hydrogen. You decide to put these atoms to use by making methane, ethane, propane, and butane molecules. Each molecule of methane uses one carbon and four hydrogen atoms. Each molecule of ethane uses two carbon and six hydrogen atoms. Each molecule of propane uses three carbon and eight hydrogen atoms. Each molecule of butane uses four carbon and ten hydrogen atoms. Assuming you use all of your atoms, the question is: what combinations of molecules are possible? Of course, we would allow solutions with, say, no butane, but 3 or 1.4 butane are not permitted. There are multiple answers – be sure to list them all, for example “3 methane, 5 ethane, 0 propane, and 2 butane” would be a proper form for one of your answers (although this example turns out not to work). We are interested only in whole number solutions – please do not split the atom. That’s just dangerous.

Explanation / Answer

total no of methanes = m , total no of ethanes = e , total no of propane = p, total no of butane = b

As we know total number of carbon atoms = 40

so, m +2e+3p+4b = 40

similarly 4m+6e+8p+10b = 150

and m.e.p,b are positive integar or zero

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