I have libboost but they're an older version than the one that bitcoin-qt requires. (I have the 1.49, bitcoin-qt requires the 1.55)
How to solve it?
Well, that would depend on what version of ubuntu you're using. I guess it's not Trusty if it comes with libboost 1.49 installed..
https://launchpad.net/~boost-latest/+archive/ppaThere's 1.55 for saucy, quantal, and precise.
If you're on trusty (maybe saucy and quantal too?), you could just sudo aptitude install libboost1.55-all-dev and libboost1.55-dev, and it'll take care of removing the old version of libboost.. or you could just purge it yourself.