The process for finding a solution is as follows:

There are infinite solutions, if we consider all rational numbers as possible prices. Picking a percentage for the first discount, let's say #a%#, since #1/50# is #2%#, we find that the price after the first discount is #50 - a/2# dollars. This means that #0 < a < 40#. If the resulting price is #p# (after the first discount), we need to find what percentage the second discount is, so that the final price is #30#. If the second percentage is #b#, then #b = 100(p-30)/p#, or:

#100(50-a/2-30)/(50-a/2) = 100(40-a)/(100-a)#.

Since #0 < a < 40#, a #b# is always defined. So there are indeed infinite solutions.