A trader has a beam balance and two weight weighing 25 grams and 60 grams using the theory diophantine equations, shows how he can sell exactly 40 grams of flour, using only these two weights and balance.
I got infinity number of solutions therefore it's not sure, give me a hint to restriction the solution if it is possible
Thank you!!
I see only $4$ possible measures of flour where $F_n$ is flour-weight and one or more $numbers$ are the weights.
$$F_{25}=25\quad F_{40}+25=65\quad F_{65}=65\quad F_{90}=25+65\quad $$
I see no need for diophantine equations. but
$8F+5a=13b$ works if $ F=a=c=5\quad$ or $\quad5f+5a=5b\implies f=8,\space a=5,\space b=13$.
Is this the sort of thing giving you trouble? Perhaps the equation they are looking for is simply $f+a=b$. Let me/us know what you've tried.