The easiest way to do this is to work out the lowest common multiple of 10 and 1 by listing the multiples:
12: 12,24,36,48,60,72
10: 10,20,30,40,50,60
We can then see that the lowest number of plates and cups is 60 of each.
We can then work out the costs:
Cups:
60 total = 5 packages
5 packages = $15
Plates:
60 total = 6 packages
6 packages = $30
The total cost is then $15 + $30 = $45