My local charity shop was selling off books at 3 paperbacks for $1, 2 hard back for $1 , and $2 for coffee table books, I spent $30 for 30 books and I bought at least one of each book . How many books of each type did I buy?
If $\displaystyle n_p>0$, $\displaystyle n_h>0$ and $\displaystyle n_c>0$ denote the number of paper backs, hard backs and coffee table book bought we have:
$\displaystyle n_p+n_h+n_c=30$
and
$\displaystyle \frac{n_p}{3}+\frac{n_c}{2}+2n_c=30$
Also $\displaystyle n_p$ is divisible by $\displaystyle 3$ and $\displaystyle n_c$ is divisible by $\displaystyle 2$.
Now a bit of trial and error should be sufficient to find the solution.
CB