From the question, we have:

\(a:54=c\left(r=38\right)\) and \(a:18=14\left(r\ge0\right)\)

We see from the question: \(14.18\le a\le14.18+17\) <=> \(252\le a\le269\)

If \(c=1\) in the first equation => \(a=54+38=92\left(wrong\right)\)

If \(c=2\) in the first equation => \(a=54.2+38=146\left(wrong\right)\)

............

If \(c=4\) in the first equation => \(a=54.4+38=254\left(right\right)\)

So \(a=254\) => \(r=2\).

So the answer of the question is: \(254+2=256\)

What do you mean  a gives 14 and a remainder r when divided by 18 ? I don't understand much about your question ?

Moreover, remainder not remaider :))