An alien society uses a peculiar currency called 'pibs' with just two denominations of coins - \(a + 13\) pibs coin and \(a - 9\) pibs coin. You have several of these coins. Is it possible to purchase an item that costs \(+85\) pibs?
Yes, we can use \(10\) coins of \(+13\) pibs and \(5\) coins of \(-9\) pibs to make a total of \(+85\). Using the two denominations, try to get the following totals:
(a) \(+12\) \(=\)
(b) \(-30\) \(=\)
(c) \(+24\) \(=\)
(d) \(-55\) \(=\)
[Hint: Writing down a few multiples of \(13\) and \(9\) can help.]