An approximate solution would work for the above but you can see how easily it pops up: http://en.wikipedia.org/wiki/Subset_sum_problem
Complexity theory is the coolest thing I've learned. I think thats why people study it - they don't particularly care about the practicality of their work. Which is ok. Breakthroughs and connections are often unexpected (It's hard to discuss cryptography without understanding it), so you might as well let the smart people do whatever they feel like in academia than declare x,y,z to be the 'real' issues people are facing that should be solved - we have the market/industry for that.
Incidentally, I wasted a lot of time thinking about http://en.wikipedia.org/wiki/Partition_problem in high school - I was trying to figure out how to make the A-side and B-side of a mix tape of equal length.